Help with this question?

This exercise is about normal matrices. A (square complex, say, d X d) matrix M is called normal if M M l = M lM . A fundamental theorem about such matrices says that M is normal if'rr it is diagonah'zable in some orthonormal basis (k)g=1 of Cd, La, :1 M = Z: cklzpkxwu (2) k=1 (a) Find an expression similar to (2) for M l and verify that matrices of form (2) are indeed normal. (This is the easy direction of the fundamental theorem referenced to above, the hard direction is assumed.) (b) What are the eigenvalues of M? M l? M M l ? (c) Deduce that unitary matrices are diagonalizable and that their eigenvalues are of absolute value 1