1. The problem statement, all variables and given/known data Let m < n. Let A be an n × m matrix, and let B be an m × n matrix. Prove that AB /= In . 2. Relevant equations 3. The attempt at a solution since m<n, the reduced form of matrix B will have free variables. I know that if A and B are invertible matrices, AB will be as well but does the converse also hold?