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

Dear Student,
Please find below the solution to your problem.

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.

Thanks and Regards