Title says it all. I was thinking of using the fact that the determinant and the trace are thesame , but I don't know how to proceed.
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Hint: Assuming that $M$ is invertible, $M^{-1}(MN)M = NM$. Two conjugated matrices always have the same eigenvalues. – Jack D'Aurizio Nov 11 '15 at 15:24
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Actually, this has been asked so many times (with enlightening different answers): http://math.stackexchange.com/questions/311342/do-ab-and-ba-have-same-minimal-and-characteristic-polynomials?lq=1, http://math.stackexchange.com/questions/1173614/eigenvalues-of-ab-and-ba-qquad?lq=1, http://math.stackexchange.com/questions/821934/eigenvalues-of-ab-and-ba-matrices?lq=1, http://math.stackexchange.com/questions/1050372/is-it-true-that-sigmaab-sigmaba?lq=1 among them. – Martin Argerami Nov 11 '15 at 15:43