Question

If $A$ is non-singular matrix and $(A+I)(A-I)=0$ then $A+A^{-1}=$ .........

• A. $2A$
• B. $0$
• C. $I$
• D. $3I$

Answer 1

Answer: (A)

We have, $A$ is non-singular matrix
$\therefore |A|=0$
and $(A+I)(A-I)=0$
$\Rightarrow A^2-I^2=0$
$\Rightarrow A^2=I^2=1$
$\Rightarrow A.A=I\Rightarrow A^{-1}=A$
$\therefore A+A^{-1}=A+A=2A$