Question

If A is a square matrix such that │A│≠0 and A² – A + 2I = 0 then A^-1 = ? 

A. (I-A) 

B. (I+A)

C. 1/2(I - A)

D. 1/2 (I + A)

Answer 1

2 – A + 2I = 0 

Multiplying by A^-1 

A^-1A² – A^-1A + 2I A^-1 = 0 

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

A^-1 = 1/2(I - A)