Hey, I'm wondering if I have a known set of eigenvalues (-1, +1, 0) for A, if I can prove that the matrix A = A3? I can prove that if A3 = A, that the eigenvalues would be −1, +1, and 0. The following is the proof: A*k=lambda*k A3*k=lambda3*k Since A=A3, A*k=A3*k lambda*k=lambda3*k lambda*k - lambda3*k = 0 lambda - lambda3 = 0 lambda*(1-lambda2) = 0 lambda = 0, -1, +1 Is there any way to prove it the other way around? If I know that the eigenvalues are 0, -1, and +1, can I prove that A3 = A? Thanks!