Question

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

• A. A + I
• B. A
• C. A - I
• D. I - A

Answer 1

Answer: (D)

I - A

Answer 2

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