Question

If matrix $A$ is non-singular and satisfies $A^2-A+I=O,$ then the inverse of $A$ is equal to

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

Answer 1

The correct option is C $I-A$

Given: $A^2-A+I=O$
$\Rightarrow I=A-A^2$
$\Rightarrow I{A}^{-1}=A{A}^{-1}-A^2{A}^{-1}$
$\Rightarrow A^{-1}=I-A\cdot A{A}^{-1}=I-AI$
$\Rightarrow A^{-1}=I-A$