If A is a non-diagonal involutory matrix- thenA - I - 0A - I-is non zero singularnone of theseA - I - 0

The correct option is B A I is non zero singularA^2=I ⇒ A^2 I=0 ⇒ (A+I)(A I)=0 ∴ either | A+I |=0 or | A I |=0 If | A I | ≠ 0, then (A+I)(A I)=0 ⇒ A+I=0 w ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Involutory Matrix

If A is a non...

Question

If A is a non-diagonal involutory matrix, then

A - I = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A + I = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A - I is non zero singular

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

none of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C A - I is non zero singular
$A^{2} = I \Rightarrow A^{2} - I = 0$
$\Rightarrow$ (A+I)(A-I)=0
$∴$ either $| A + I | = 0$ or
$| A - I | = 0$
If $| A - I | \neq 0$ , then $(A + I) (A - I) = 0 \Rightarrow A + I = 0$ which is not so
$∴ | A - I |$ and $A - I \neq 0$ .

Suggest Corrections

Similar questions

Q. If

A

is a non-diagonal involutory matrix, then

Q. If A is involutory matrix and I is unit matrix of same order, then (I - A)(I + A) is

If $A$ is a $2 \times 2$ matrix with non - zero entries let $A^{2} = I$ , where $I$ is $2 \times 2$ identity matrix.

Define $t r (A) =$ Sum of diagonal element of $A$ and $| A | =$ Determinant of matrix $A$ .

Statement I $t r (A) = 0$ .

Statement II $| A | = i$

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. If

A

is an involutory matrix and

(I + A)^{n} = a I + b A, (I is unit matrix), a, b \in R .

Then

(a + b) =

Join BYJU'S Learning Program

If A is a non-diagonal involutory matrix, then

The correct option is C A - I is non zero singularA2=I⇒A2−I=0 ⇒ (A+I)(A-I)=0 ∴ either |A+I|=0 or |A−I|=0 If |A−I|≠0, then (A+I)(A−I)=0⇒A+I=0 which is not so ∴|A−I| and A−I≠0.

The correct option is C A - I is non zero singular
$A^{2} = I \Rightarrow A^{2} - I = 0$
$\Rightarrow$ (A+I)(A-I)=0
$∴$ either $| A + I | = 0$ or
$| A - I | = 0$
If $| A - I | \neq 0$ , then $(A + I) (A - I) = 0 \Rightarrow A + I = 0$ which is not so
$∴ | A - I |$ and $A - I \neq 0$ .