Let A be a 7×7 matrix where each entry is either 0 or 1.
a) Argue that each entry of the matrix A^k are less than 7k and requires O(k) bits each.
b) give an algorithm that computes the matrix A^n for a given n with running time O(n^log_2 (3)) (use Karatsuba's integer multiplication algorithm as a subroutine.)