Two questions. First, I'm given a 3x3 matrix with the last row all zeroes. I'm asked to diagonalizable it, but the determinant is 0, so there are no eigenvalues. Am I reasoning correctly here? It seems an odd question to ask. Second, I'm asked to prove that if A n x n matrix in C space, then if A has n distinct eigenvalues, A is then diagonalizable. The way I proved it is to say that for A to be diagonalizable, it must have n distinct eigenvectors, which is only the case if it has n distinct eigenvalues. This seems far too easy, am I missing something?