How to prove a matrix not invertible? How can I prove that A*B is not invertible when A (mXn) and B (nXm) 

while (m>n)?
Hint: A Matrix is invertible iff it is square and has full Rank
HINT: Complete $A$ to $\tilde A$ by adding  on the right $m-n$ columns consisting of $0$'s, and $B$ to $\tilde B$ by adding below $m-n$ rows consisting of $0$'s. Observe that $A\cdot B = \tilde A \cdot \tilde B$. 
Now clearly $\det \tilde A = \det \tilde B = 0$, so $\det AB = 0$.