Denote the columns of In by e1, e2,..., en. Row reduction of [A I] to [I A^-1] can be viewed as the simultaneous solutions of the n systems: ___________________ where the 'augmented columns of these systems have been placed next to A to form [A e1 e2 ... en]= [A I]. The equation _________________and the definition of matrix multiplication show that the columns of ________are precisely the solutions of the the above systems.