Question

A square, non-singular matrix $A$ satifies $A^2-A+2I=0$, then $A^{-1}=$

• A. $I-A$
• B. $\frac{(I-A)}{2}$
• C. $I+A$
• D. $\frac{(I+A)}{2}$

Answer 1

The correct option is B $\frac{(I-A)}{2}$

Given, $A^2-A+2I=0$

$\Rightarrow 2I=A-A^2$

$\Rightarrow 2A^{-1}I=A^{-1}A-A^{-1}{A}^2$

$\therefore A^{-1}=\frac{I-A}{2}$