# which are diagonalizable over $\mathbb{C}$

a) Unitary matrices are normal matrix hence diagonalizable as a consequence of spectral theorem

b)same as a)

c)No idea.but I think it may not be diagonalizable unless it has one eigen value with dimension of eigen space $1$

d) No idea.

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Hint: The shear matrix $$\left[\begin{array}{cc} 1 & 1\\ 0 & 1 \end{array}\right]$$ has two real eigenvalues (both equal $1$) complex entries, and cannot be diagonalized.
@Kuttus: $a$ and $b$ are correct. –  Eric Naslund Dec 18 '12 at 18:07