If A^2-A+I=0, then A^-1 is equal to :

The correct answer is Option (4) → $I-A$

$A^2-A+I=0$

multiplying by $A^{-1}$

$A^{-1}A^2-A^{-1}A+^{-1}I=0$ (we know that $A^{-1}A=I$ and $AI = A$)

so $A-I+A^{-1}=0$ 

so $A^{-1}=I-A$