If $A$ is an $m \times n$ and $B$ is an $n \times m$ matrix with $n < m$ then prove that $C = AB$ is not invertible.
I am not getting any idea. May be I am missing vary basic point. $C = AB$ where both $A$ and $B$ are square matrices will be invertible iff both $A$ and $B$ be invertible. I know it and its proof.
May be this question has been discussed earlier, but I am not seeing the link. Thank you for your help.