Am I being stupid? This seems like an easy question, especially given all the linear algebra I've been doing so far. For some reason, this has me stumped.

Given a real matrix A, I have to prove that $\displaystyle {A^t}A$ is diagonalizable ($\displaystyle {A^t}$ being the transpose of A). The other questions that I've already done are about inner product spaces, although this question may be independent of that.