Problem 8.3 (2 points). Let A E Rx" be the adjacenty matrix of a graph G. We define a 1 H(k) : . We will prove that H(k) holds for all k by induction, that is, we will first prove that H(1) is true. Then we will prove that if H(k) is true for some k, then H(k + 1) is true. Combining these two things, we get that H(2) holds, hence H(3) holds, hence H(4) holds... and therefore H(k) will be true for all k 2 1. (a) Show that H(1) is true. (b) Show that if H(k) is true for some k, then H(k + 1) is also true