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which are diagonalizable over $\mathbb{C}$

Which of the following matrices are diagonalizable over $\mathbb{C}$.
(a) Any $n×n$ unitary matrix with complex entries.
(b) Any $n×n$ hermitian matrix with complex entries.
(c) Any $n×n$ strictly upper triangular matrix with complex entries.
(d) Any $n×n$ matrix with complex entries whose eigenvalues are real.

how to solve this problem.can you help me please?thanks for your help.

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    Welcome to math.SE! Please consider taking the time to read the [faq] to familiarise yourself with some of our common practices. As this question appears to be homework, please consider reading [this page](http://meta.math.stackexchange.com/q/1803/8348) for information about asking _effective_ homework-related questions. Cheers!2012-12-24
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    this is a question from a question paper which i got from someone and try to solve it for my own interest but could not solve.so i post it here. so for any help from you i shall be greatful to you2012-12-24
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    Surely you can find a non-diagonalizable example of (c), if you have ever seen a non-diagonalizable matrix. Can't you?2012-12-24
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    Also (d) is clearly non-true...$$\begin{pmatrix}1&1\\0&1\end{pmatrix}$$ adn, btw, given also a counterexample for (c)2012-12-24

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