Let a square matrix of order n satisfy the square of a - 5A + 7e = 0, prove that 3e-a is invertible, and find the inverse matrix of (3a-e)

Let a square matrix of order n satisfy the square of a - 5A + 7e = 0, prove that 3e-a is invertible, and find the inverse matrix of (3a-e)

A*A - 5A +7E
= A(A-3E) - 2A +7E
= A(A-3E) -2(A-3E)+E
=(A-2E)(A-3E)+E
=0
∴(A-3E)(E-2A)=E
The inverse matrix is e-2a