Suppose $A$ and $B$ are real or complex $n \times n$ matrices and $C = [A,B]$ is their commutator. If $C$ commutes with $A$, show that $C$ is nilpotent.
Matrix commuting with commutator
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linear-algebra
matrices
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5Please specify where the question is from, and what you've tried so far. Welcome! – 2012-10-30
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2This is a very common problem in linear algebra that can be found in many places (with solution). See [here](http://www.imc-math.org.uk/imc2009/imc2009-day2-solutions.pdf). – 2012-11-05