Let a square matrix of order n satisfy a ^ 2-3a + 3E = 0, prove that a-2e is invertible, and find its inverse matrix?

Let a square matrix of order n satisfy a ^ 2-3a + 3E = 0, prove that a-2e is invertible, and find its inverse matrix?

Certificate:
A²-3A+3E=0
A²-3A+2E=-E
(A-2E)(A-E)=-E
(A-2E)(E-A)=E
So a-2e is reversible
The inverse matrix of a-2e is e-a

Elden Ring Premiere

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