8. The purpose of this exercise is to outline a proof by induction of part (1) of Theorem 3.3. Because Theorem 3.3 is used extensively to prove further results in the textbook, in the following proof you may not use any results that appear after Theorem 3.3 in order to avoid circular reasoning. Let A be an nxn matrix, let R be the row operation (i) c (i), and let B = R(A). (a) Prove |B|=c|A| when n = 1. (This is the Base Step.) (b) State the inductive hypothesis for the Inductive Step. (c) Complete the Inductive Step for the case in which R is not performed on the last row of A. (d) Complete the Inductive Step for the case in which R is performed on the last row of A.