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Let $A\in M_{n}(C)$ and $A^{n}=2A$ with $n>1$. I need to show that $A$ is diagonalizable.

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    The title of your question seems misleading to me: the answer to the question asked in the title is clearly no, but in your question there is an additional hypothesis.2012-12-11
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    What happens when you use the Jordan decomposition?2012-12-11

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