I have been given the matrix $A$ and we are told it is a $5\times 5$ matrix s.t. $A^4=A^2\neq A$. I want to find the eigenvalues so I tried $A^2(A-I)(A+I)=0$ so the eigenvalues are $0, 1, -1$ but I don't think this is right, I think I have missed some. The whole question is wanting to find the possible characteristic and minimal polynomials of $A$ hence my want to find the e-values. Am I doing it right? I have seen this sort of problem before where you have a matrix equal to some power of itself or similar and I can never do them, any hints on how to do this or similar problems would be useful, thank you!
2026-04-17 12:59:11.1776430751
Eigenvalues of 5x5 matrix given equation involving matrix
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