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## Homework Statement

Let A[itex]\in[/itex]M[itex]_{n}[/itex]([itex]\Re[/itex]) a matrix verifying

A[itex]^{3}[/itex]-A[itex]^{2}[/itex]-I[itex]_{n}[/itex]=0

a) Show that A is inversible and calculate it

b) Show that the solution X[itex]\subset[/itex]M[itex]_{n}[/itex]([itex]\Re[/itex]) of the equation

A[itex]^{k}[/itex](A-I[itex]_{n}[/itex])X=I[itex]_{n}[/itex]

has a unique solution.

## The Attempt at a Solution

I'm having trouble with starting this one. I'm quite rubbish with these matrices in linear algebra, but I have exams in a few days and this question was on it, so i need help!

I know the criteria for matrix inverse (AB=BA=I). However there's too much going on... help me dissect it? thanks a lot to anyone for any help, much appreciated.