3. Fast Matrix Multiplication. Given two n x n matrices X, Y of integers, their product is another n n matrix Z with, 1 Naively, computing Z seems to take 0(n3) time since there are n2 entries, and computing the value for a single entry involves n addition operations. In this problem, we'll develop a faster matrix multiplication algorithm. For simplicity, assume that n is a power of 2. (a) First, define eight n/2x n/2 matrices A, B,C, D,E, F.,G, H so that A B E F G H Prove that, CE +DG CF +DH