Rank, and existence of Matrices Let $A$ be an $m\times n$ matrix.  If the rank of $A$ is $m$, then prove there exists a matrix $B$, wich is $n \times m$, such that $AB=\text{I}_m$

Hint:
try to prove that there are matrices $P,Q$ such as
$
A = P \bigl(\begin{smallmatrix}
I_m & 0
\end{smallmatrix} \bigr)Q^{-1}
$.
