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## Homework Statement

Let A be an n×n matrix which has the property that A^2 =A.

(i) Write down the most general polynomial in A

## Homework Equations

## The Attempt at a Solution

My biggest problem is that I don't even understand what the question is asking

Is it just sum (alphaA^n)=0

but A^n=A

sum(alpha A)=0 ?

I know its not the equation to find the eigenvalues as that follows, and I'm fine with that

Av=pv where p are the eigenvalues, and v the corresponding eigenvectors

A^2v=Apv

Av=p(Av)

pv=p^2v

v(p)(p-1)=0 and hence p= 0 or 1

But I just don't understand the first bit

Many thanks in advance :)