RD Sharma Solutions For Class 12 Maths Exercise 7.1 Chapter 7 Adjoint and Inverse of a Matrix

RD Sharma Solutions for Class 12 Maths Exercise 7.1 Chapter 7 Adjoint and Inverse of a Matrix is provided here. The solutions for the exercise wise answers are prepared by the experts at BYJU’S in the best possible way which are easily understandable by students.

The PDF of RD Sharma Solutions for Class 12, Exercise 7.1 of Chapter 7 Adjoint and Inverse of a Matrix can be downloaded from the given links. This exercise consists of two levels according to the increasing order of difficulties. Let us have a look at the important topics covered in this exercise.

  • Definition and meaning of adjoint of a square matrix
  • The inverse of a matrix
  • Some useful results on invertible matrices
  • Determining the adjoint and inverse of a matrix
  • Determining the inverse of a matrix when it satisfies the matrix equation
  • Finding the inverse of a matrix by using the definition of inverse
  • Finding a non – singular matrix when adjoint is given

RD Sharma Solutions For Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Exercise 7.1:-Download PDF Here

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RD Sharma Class 12 Maths Chapter 7 Exercise 1 45

Access another exercise of RD Sharma Solutions For Class 12 Maths Chapter 7 – Adjoint and Inverse of a Matrix

Exercise 7.2 Solutions

Access answers to Maths RD Sharma Solutions For Class 12 Chapter 7 – Adjoint and Inverse of a Matrix Exercise 7.1

1. Find the adjoint of each of the following matrices:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 2

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 4

Verify that (adj A) A = |A| I = A (adj A) for the above matrices.

Solution:

(i) Let

A =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 5

Cofactors of A are

C11 = 4

C12 = – 2

C21 = – 5

C22 = – 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 6

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 7

(ii) Let

A =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 8

Therefore cofactors of A are

C11 = d

C12 = – c

C21 = – b

C22 = a

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 9

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 10

(iii) Let

A =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 11

Therefore cofactors of A are

C11 = cos α

C12 = – sin α

C21 = – sin α

C22 = cos α

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 12

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 13

(iv) Let

A =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 14

Therefore cofactors of A are

C11 = 1

C12 = tan α/2

C21 = – tan α/2

C22 = 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 15

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 16

2. Compute the adjoint of each of the following matrices.

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 17

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 18

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 19

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 20

Solution:

(i) Let

A =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 21

Therefore cofactors of A are

C11 = – 3

C21 = 2

C31 = 2

C12 = 2

C22 = – 3

C23 = 2

C13 = 2

C23 = 2

C33 = – 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 22

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 23

(ii) Let

A =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 24

Cofactors of A

C11 = 2

C21 = 3

C31 = – 13

C12 = – 3

C22 = 6

C32 = 9

C13 = 5

C23 = – 3

C33 = – 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 25

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 26

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 27

(iii) Let

A =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 28

Therefore cofactors of A

C11 = – 22

C21 = 11

C31 = – 11

C12 = 4

C22 = – 2

C32 = 2

C13 = 16

C23 = – 8

C33 = 8

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 29

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 30

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 31

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 32

(iv) Let

A =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 33

Therefore cofactors of A

C11 = 3

C21 = – 1

C31 = 1

C12 = – 15

C22 = 7

C32 = – 5

C13 = 4

C23 = – 2

C33 = 2

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 34

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 35

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 36

Solution:

Given

A =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 37

Therefore cofactors of A

C11 = 30

C21 = 12

C31 = – 3

C12 = – 20

C22 = – 8

C32 = 2

C13 = – 50

C23 = – 20

C33 = 5

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 38

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 39

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 40

Solution:

Given

A =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 41

Cofactors of A

C11 = – 4

C21 = – 3

C31 = – 3

C12 = 1

C22 = 0

C32 = 1

C13 = 4

C23 = 4

C33 = 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 42

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 43

Solution:

Given

A =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 44

Cofactors of A are

C11 = – 3

C21 = 6

C31 = 6

C12 = – 6

C22 = 3

C32 = – 6

C13 = – 6

C23 = – 6

C33 = 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 45

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 46

Solution:

Given

A =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 47

Cofactors of A are

C11 = 9

C21 = 19

C31 = – 4

C12 = 4

C22 = 14

C32 = 1

C13 = 8

C23 = 3

C33 = 2

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 48

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 49

7. Find the inverse of each of the following matrices:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 50

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 51

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 52

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 53

Solution:

(i) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

Now, |A| = cos θ (cos θ) + sin θ (sin θ)

= 1

Hence, A – 1 exists.

Cofactors of A are

C11 = cos θ

C12 = sin θ

C21 = – sin θ

C22 = cos θ

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 54

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 55

(ii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

Now, |A| = – 1 ≠ 0

Hence, A – 1 exists.

Cofactors of A are

C11 = 0

C12 = – 1

C21 = – 1

C22 = 0

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 56

(iii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 57

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 58

(iv) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

Now, |A| = 2 + 15 = 17 ≠ 0

Hence, A – 1 exists.

Cofactors of A are

C11 = 1

C12 = 3

C21 = – 5

C22 = 2

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 59

8. Find the inverse of each of the following matrices.

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 60

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 61

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 62

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 63

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 64

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 65

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 66

Solution:

(i) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 67

= 1(6 – 1) – 2(4 – 3) + 3(2 – 9)

= 5 – 2 – 21

= – 18≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 5

C21 = – 1

C31 = – 7

C12 = – 1

C22 = – 7

C32 = 5

C13 = – 7

C23 = 5

C33 = – 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 68

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 69

(ii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 70

= 1 (1 + 3) – 2 (– 1 + 2) + 5 (3 + 2)

= 4 – 2 + 25

= 27≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 4

C21 = 17

C31 = 3

C12 = – 1

C22 = – 11

C32 = 6

C13 = 5

C23 = 1

C33 = – 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 71

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 72

(iii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 73

= 2(4 – 1) + 1(– 2 + 1) + 1(1 – 2)

= 6 – 2

= – 4≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 3

C21 = 1

C31 = – 1

C12 = + 1

C22 = 3

C32 = 1

C13 = – 1

C23 = 1

C33 = 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 74

(iv) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 75

= 2(3 – 0) – 0 – 1(5)

= 6 – 5

= 1≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 3

C21 = – 1

C31 = 1

C12 = – 15

C22 = 6

C32 = – 5

C13 = 5

C23 = – 2

C33 = 2

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 76

(v) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 77

= 0 – 1 (16 – 12) – 1 (– 12 + 9)

= – 4 + 3

= – 1≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 0

C21 = – 1

C31 = 1

C12 = – 4

C22 = 3

C32 = – 4

C13 = – 3

C23 = 3

C33 = – 4

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 78

(vi) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 79

= 0 – 0 – 1(– 12 + 8)

= 4≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = – 8

C21 = 4

C31 = 4

C12 = 11

C22 = – 2

C32 = – 3

C13 = – 4

C23 = 0

C33 = 0

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 80

(vii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 81 – 0 + 0

= – (cos2 α – sin2 α)

= – 1≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = – 1

C21 = 0

C31 = 0

C12 = 0

C22 = – cos α

C32 = – sin α

C13 = 0

C23 = – sin α

C33 = cos α

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 82

9. Find the inverse of each of the following matrices and verify that A-1A = I3.

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 83

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 84

Solution:

(i) We have

|A| =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 85

= 1(16 – 9) – 3(4 – 3) + 3(3 – 4)

= 7 – 3 – 3

= 1≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 7

C21 = – 3

C31 = – 3

C12 = – 1

C22 = 1

C32 = 0

C13 = – 1

C23 = 0

C33 = 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 86

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 87

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 88

(ii) We have

|A| =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 89

= 2(8 – 7) – 3(6 – 3) + 1(21 – 12)

= 2 – 9 + 9

= 2≠ 0

Hence, A – 1 exists

Cofactors of A are

C11 = 1

C21 = 1

C31 = – 1

C12 = – 3

C22 = 1

C32 = 1

C13 = 9

C23 = – 5

C33 = – 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 90

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 91

10. For the following pair of matrices verify that (AB)-1 = B-1A-1.

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 92

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 93

Solution:

(i) Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 94

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 95

Hence, (AB)-1 = B-1A-1

(ii) Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 96

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 97

Hence, (AB)-1 = B-1A-1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 98

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 99

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 100

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 101

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 102

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 103

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 104

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 105

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 106

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 107

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 108

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 109

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 110

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 111

Solution:

Given

A =
https://gradeup-question-images.grdp.co/liveData/PROJ23872/1543574054891449.png and B – 1 =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 113

Here, (AB) – 1 = B – 1 A – 1

|A| = – 5 + 4 = – 1

Cofactors of A are

C11 = – 1

C21 = 8

C31 = – 12

C12 = 0

C22 = 1

C32 = – 2

C13 = 1

C23 = – 10

C33 = 15

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 114

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 115

(i) [F (α)]-1 = F (-α)

(ii) [G (β)]-1 = G (-β)

(iii) [F (α) G (β)]-1 = G (-β) F (-α)

Solution:

(i) Given

F (α) =
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 116

|F (α)| = cos2 α + sin2 α = 1≠ 0

Cofactors of A are

C11 = cos α

C21 = sin α

C31 = 0

C12 = – sin α

C22 = cos α

C32 = 0

C13 = 0

C23 = 0

C33 = 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 117

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 118

(ii) We have

|G (β)| = cos2 β + sin2 β = 1

Cofactors of A are

C11 = cos β

C21 = 0

C31 = -sin β

C12 = 0

C22 = 1

C32 = 0

C13 = sin β

C23 = 0

C33 = cos β

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 119

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 120

(iii) Now we have to show that

[F (α) G (β)] – 1 = G (– β) F (– α)

We have already know that

[G (β)] – 1 = G (– β)

[F (α)] – 1 = F (– α)

And LHS = [F (α) G (β)] – 1

= [G (β)] – 1 [F (α)] – 1

= G (– β) F (– α)

Hence = RHS

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 121

Solution:

Consider,

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 122

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 123

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 124

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 125

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 126

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 127

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 128

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 129

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 130

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