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

• Matrices Determinants

If  A² – A + I = 0, then the inverse of A is

1. A - I
2. A
3. I + A
4. I - A

Answer

A² – A + I = 0

I = A – (A × A)

IA^-1 = AA^-1 – A(AA^-1)

A^-1 = I - A

The correct option is D.