If A is a 2 - 2 matrix and A2 - I where A I- A -I then which of the following is necessarily true-

The correct option is D Tr(A) =0 and |A| = 1 Given, A is a 2× 2 matrix such that, A^2=I then |A|=1 |A^2|=±1 Tr(A)=0 ...

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Byju's Answer

Standard XII

Mathematics

Definition of a Determinant

If A is a ...

Question

If $A$ is a $2 \times 2$ matrix and $A^{2} = I$ where $A \neq I, A \neq - I$ then which of the following is necessarily true?

T r (A) = 0

and

| A | = 1

- 1

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T r (A) = 0

and

| A | = 1

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T r (A) \neq 0

and

| A | = - 1

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T r (A) = 0

and

| A | = - 1

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Solution

The correct option is D $T r (A) = 0$ and $| A | = - 1$
Given,
$A$ is a $2 \times 2$ matrix such that,
$A^{2} = I$

then
$| A | = 1 ⟹ | A^{2} | = \pm 1$
$T r (A) = 0$

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Similar questions

Q. Let A be a

2 \times 2

matrix with non-zero entries and let

A^{2} = I

, where I is

2 \times 2

identity matrix. Define Tr(A)

=

sum of diagonal elements of A and

| A | =

determinant of matrix A.
Statement-1 Tr(A)

= 0

Statement-2:

| A | = 1

Q. Assertion :Let

A

be a

2 \times 2

matrix with real entries. Let

I

be the

2 \times 2

identity matrix. Denote by

t r (A)

, the sum of diagonal entries of

A

. Assume that

A^{2} = I

A \neq I

and

A \neq - I

, then

d e t (A) = - 1

Reason: If

A \neq I

and

A \neq - I

, then

t r (A) \neq 0

Q. If

A

2 \times 2

matrix such that

A^{2} = 0

, then

t r (A)

Q. Let A be a

2 \times 2

matrix with real entries. Let I be the

2 \times 2

identity matrix. Denote by tr(A), the sum of diagonal entries of

A

. Assume that

A^{2} =

I.
Statement-l: If

A \neq I

and

A \neq - I

, then

det A = - 1

.
Statement-2: If

A \neq I

and

A \neq - I

, then

t_{1} {A) \neq 0

Q. Let

A

be a

2 \times 2

matrix with real entries, Let I be the

2 \times 2

identity matrix. Denote by

t r (A),

the sum of diagonal entries of

A

. Assume that

A^{2} = I

Statement

1 :

A \neq I

and

A \neq - I

, then det

A = - 1

Statement

2 :

A \neq I

and

A \neq - I

, then

t r (A) \neq 0,

then which of the following is correct

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If A is a 2×2 matrix and A2=I where A≠I,A≠−I then which of the following is necessarily true?

The correct option is D Tr(A)=0 and |A|=−1Given,A is a 2×2 matrix such that,A2=Ithen|A|=1⟹|A2|=±1Tr(A)=0

If $A$ is a $2 \times 2$ matrix and $A^{2} = I$ where $A \neq I, A \neq - I$ then which of the following is necessarily true?

The correct option is D $T r (A) = 0$ and $| A | = - 1$
Given,
$A$ is a $2 \times 2$ matrix such that,
$A^{2} = I$

then
$| A | = 1 ⟹ | A^{2} | = \pm 1$
$T r (A) = 0$