Let A be an mxn matrix with rank m. Prove that there exists an nxm matrix B such that AB = $I_{m}$.
-Since the rank of A is m, and A is an mxn matrix, the matrix must have full row rank, so there must also exist some $b_{j}$ that satisfies the equation A$b_{j}$= $I_{j}$, where j stands for the jth column of a matrix.