Condition for $\det(A^{T}A)=0$ Is it always true that
$\det(A^{T}A)=0$, $\hspace{0.5mm}$ for $A=n \times  m$ matrix with $n<m$?
From some notes I am reading on Regression analysis, and from some trials, it would appear this is true.
It is not a result I have seen, surprisingly.
Can anyone provide a proof?
Thanks.

hint
$\mathrm{Rank}(AB)\leq \min (\mathrm{Rank} A, \mathrm{Rank}B)$
Notice that $A^{\mathrm{T}}A$ is $m\times m$
