Main Question or Discussion Point
Prove that if A is an mXn matrix, there is an invertible matrix C such that CA is in reduced row-echelon form. I think I know how to get the inverse of a square or an nXn matrix B, i.e., each elementary row operation carried out on B is also carried out on an identity matrix I. [B|I] to give [I|B^-1]. But I have no idea how to do the same to an mXn matrix A in order to find C. In fact are all mXn matrices invertible? I doubt it. I am studing this on my own, so please give a hint or two to get started. Thanks.