Question

Let $A$ be a non-singular symmetric matrix of order $3$ . If $A^T=A^2-I$ , then ${\left(A-I\right)}^{-1}$ is equal to

• A. $A$
• B. $2A$
• C. $A-I$
• D. $2A-I$

Answer 1

Answer: (A)

$\because A^T=A$ (as $A$ is symmetric)
$\therefore A=A^2-I\Rightarrow A^2-A=I$
$\Rightarrow I=A\left(A-I\right)=\left(A-I\right)A$
$\Rightarrow {\left(A-I\right)}^{-1}=A$