Answer to Question #27498 in Linear Algebra for Yee-Chen Sheng

Question #27498
k is an eigenvalue of S iff det(S-kI) = 0, and det(AB) = det(A)det(B). Use these facts to show that k^2 is an eigenvalue of S^2 iff either k or -k is an eigenvalue of S. Then use this result to show that p(S)^2 = p(S^2).
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