Let A and B be 2x2 matrices s.t. AB=I . Then how can I prove that BA=I? I assumed that there must exist some sequence of elementary row operations which carries B into I, and I denoted this sequence by the matrix A. But here, I realized there's some pieces that I' m missing, which I colored red. How can I explain it ? or is the way of proving this statement even valid? Somebody help me plz!!!!