Suppose $A$ is an $n \times n$ matrix. Show that $AA^{*}=I$ if and only if the rows of $A$ form an orthonormal basis.
So far the only thing that I have done with this problem is knowing that $(AA^{*})_{ij}=\langle v_i, v_j\rangle$ for all $i$ and $j$. But I do not know how to get that this in fact equals $0$ and how to show that the norm of each row is $1$. Any help is appreciated. Thanks in advance.