Let $A\in M_{m,n}$ and $m>n$. Can rank of $AA^T$ cannot be greater than rank of $A$? And is $AA^T$ singular matrix?
I think both of these are correct, since I tried some examples, but I can't prove them.
EDIT:
I've figured out that ranks have to be the same since $ker(A)=ker(AA^T)$.