If $A$ is chosen uniformly at random over all possible $m \times n$ (0,1)-matrices, what is the expected size of the absolute value of the determinant of $AA^T$. We can assume $m < n$ and all arithmetic is over the reals.

In Expected determinant of a random NxN matrix the expected size of the determinant for random (0,1) matrices was given as $\sqrt{(n+1)!}/ 2^n$ by David Speyer.

As pointed out by Richard Stanley, my question is incorrect in its reference to the related problem solved by David Speyer (and others). I should have said that when $A$ is a random $n$ by $n$ (0,1)-matrix then $\sqrt{E((\det A)^2)} = \sqrt{(n+1)!}/ 2^n$