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Apr 13, 2018 at 9:41 comment added user91684 Your proof has no interest because you don't show the equality of multiplicities of the eigenvalues of $AB,BA$. Moreover I don't see why the eigenvalue $0$ is a problem: if $\det(AB)=0$, then $\det(BA)=0$ too.
Jun 5, 2014 at 17:20 history answered user50948 CC BY-SA 3.0