(8 points) Let A E Mn (R) be given. (a) If det(A) = 1, prove that adj(adj(A)) = A. (b) If A is nonsingular, prove that adj( A) is nonsingular and adj(A) -1 = adj(A-1). (6 points) Let X = {v1, v2, . .., Un} be a subset of a vector space V over F. Let A(X) denote the set of linear combinations of the form aiv + a202 + . .. + anUn, where a; E F and an + 02+ ...+ On = 1. Prove that A(X ) is a subspace of V if and only if v. = Ov for some i E { 1, 2, ..., n}