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Let $A$ be a $10 \times 10$ matrix of complex numbers. If $A^5=I$ the identity matrix, what can be said about $A$?

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 This is a homework problem (obviously - why else the numbers $5$ and $10$ instead of $n$ and $k$?). For a hint, try diagonalization / Jordan Normal Form. The right place for such questions is math.stackexchange or artofproblemsolving. – darij grinberg Jan 7 2012 at 17:11
@darij 1. watch out for "obviously"; 2. in history many good problems were out of homework problems. If you are able to do something more glamorous and high-level, please generalize, for example to matrices of homogeneous polynomials of degree d, and change I correspondingly. – Gavriil Jan 7 2012 at 20:34
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 Thing is, MathOverflow is not for problems like this, as the FAQ will show. It is for questions at a graduate level (or upwards). I have mentioned two forums (which you can easily google up) where you can post such a problem instead. (Anyway, it is not a good homework problem, since the only thing that can be said about $A$ is that $A$ is diagonalizable and the eigenvalues of $A$ are fifth roots of unity. And both is very easy to show.) – darij grinberg Jan 7 2012 at 20:41
Hi Gavriil: I agree with the decision to close the question as it is currently written. I haven't thought about the problem yet, and probably won't, so for all I know there is interesting mathematics in the question. But the onus is on you to give some indication that there is. If this question is related to your research, you could explain your motivation and background — look over mathoverflow.net/howtoask. Homework help (at any level), though, is not the goal of MathOverflow. – Theo Johnson-Freyd Jan 8 2012 at 4:21

closed as too localized by darij grinberg, Bill Johnson, Mark Sapir, Bruce Westbury, Anthony Quas Jan 7 2012 at 18:19

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