Let A be an n×n matrix which has the property that A^2 =A.
(i) Write down the most general polynomial in A
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
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
v(p)(p-1)=0 and hence p= 0 or 1
But I just don't understand the first bit
Many thanks in advance :)