Question

12. Let a be a matrix such that ak = 0. What is the inverse of i a?

Answer 1

Answer:

Given that A2 – A + I = 0

If we multiply both sides by A-1 we have,

A-1 (A2 – A + I) = A-1 .0 = 0

Hence, A – I + A-1 = 0

This gives A-1 = -(A – I)

= I – A.