Let A be an n × n matrix.
(a) Suppose that the matrix B is obtained from A by multiplying the jth row of A by k ≠ 0. Find an elementary row operation that, when applied to B, gives A.
(b) Suppose that the matrix C is obtained from A by interchanging the jth and jth rows of A. Find an elementary row operation that, when applied to C, gives A.
(c) Suppose that the matrix D is obtained from A by adding k times the jib row of A to its jth row find an elementary row operation that, when applied to D, gives A.