Is determinant of matrix multiplied its transpose always positive?

Question

Assume $A$ is an arbitrary $m\times n$ real matrix.

Is $\det(AA^T)$ always positive? Is it non-negative or it can have any value?

Edit:

It seems I have to emphasis that $m \ne n$ i.e. matrix is non-squared.

Answer 1

In the case n=m (square matrix)

$$det(AB)=det(A)det(B)$$

and

$$det(A^T)=det(A)$$

yes, it is positive

Answer 2

If $A$ has a singular value decomposition $$ A = VDU^{-1} $$ (note since $A$ is rectangular, $V \neq U$ but $V^T = V^{-1}$ and $U^T = U^{-1}$ and finally, $D^T=D$ since $D$ is diagonal) then $$ A^T = (U^T)^{-1}D V^T = UDV^T $$ and now $$ AA^T = VD^2 V^T $$ so $\det(AA^T) = \det D^2$ which must be real but cuold be negative is one of the singular values of $A$ is complex.