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Let $A,B \in M(n,\mathbb{C})$ be two $n\times n$ matrices. I would like know how to prove that eigen-value of $AB$ is the same as the eigen-values of $BA$.

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    Is this homework? what have you tried?2012-12-19
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    A [related question](http://math.stackexchange.com/q/94926/11619). Not an exact duplicate, because there it was assumed that $B$ is invertible. Studying the answers given there will get you started anyway (more or less along the lines of Matt Pressland's +1 answer).2012-12-19

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