Question

$A$ is a square matrix and $I$ is an identity matrix of the same order. If $A^3=O,$ then inverse of matrix $\left(I-A\right)$ is

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

Answer 1

Answer: (D)

We know,
$\left(I-A\right)\left(I+A+A^2\right)=I-A^3=I$
Hence, ${\left(I-A\right)}^{-1}=I+A+A^2$