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Possible Duplicate:
Linear Algebra,regarding commutator

Let $A$ and $B$ be two $n\times n$-matrices over some field of characteristic $0$. If $A$ and $AB-BA$ commute, show that $AB-BA$ is nilpotent.

My brother asked me for help on this but I quite embarrassingly can't figure it out. I vaguely recall solving a similar problem in school, but with the added condition that $B$ also commutes with $AB-BA$.

Any help would be appreciated.

2 Answers 2