Given A $m\times n$, $\{u_1,...,u_n\}$ ON basis of $R^n$, prove eigenvalues aren't negative

Question

Given $A$ $(m\times n)$, $\{u_1,...,u_n\}$ ON(orthonormal) basis of $R^n$ which are eigenvectors of $A^TA$ with $\lambda_1 , ... , \lambda_n$ eigenvalues accordingly.

Prove: Eigenvalues are not negative, $Au_1,..,Au_n$ are orthogonal basis of $R^n$.

Any ideas, hints how to prove it are appreciated.

Edit: I believe I'll find the proof of the first part soon in the book, so I'll update as soon as possible.