The question is "give an example of a square matrix A such that A^2 is diagonalizable but A is not." I know that if A^2 is diagonalizable, A^2 = P(D^2)P^-1. And if A is not diagonalizable, there is no invertible matrix P and diagonal matrix D such that A=PDP^-1. However I'm not sure how to begin finding an example. Can someone explain how to go about finding this?