Question

If $A^2-A+I=0$ then $A^{-1}$ =

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

Answer 1

The correct option is C $I-A$

$A^2-A+I=0$

Pre- multiply with $A^{-1}$ on both sides,

$A^{-1}{A}^2-A^{-1}A+A^{-1}=A^{-1}0$

$\Rightarrow A-I+A^{-1}=0$

$\Rightarrow A^{-1}=I-A$.

option $c$ is correct.