If $A^2-A+I=0$, then the inverse of $A$ is

Question

Aicharya · Accepted Answer

Given $A^2-A+I=0$ $A^{-1} A^2-A^{-1} A+A^{-1}-I=A^{-1} \cdot 0$ (Multiplying $A^{-1}$ on both sides) $\Rightarrow A-I+A^{-1}=0$ or $A^{-1}=I-A$

Solution