2. Consider a block matrix M of size (n + m) x (n +m) of the form A B M = C D where A, B, C, D are n x n, n x m, m x n, m x m. Let I 0 N = - D- C I Calculate MN, hence prove that det(M) = det(A - BD C) det( D). Hint: you may use the fact that P Q det 0 = det (P) det ( R)