(a) Consider the following matrices A 2 B-2 13 and C- +----- 2 Compute (AB) and (BA) 2B -B -B (b) Let C be defined by CB 2B -B, where B == -B -B 2B [2]] Find the characteristic roots of C (c) Define AJ and A =I-J Show that (1) A is a symmetric and idempotent matrix (11) A2 is a symmetric and idempotent matrix (111) A A = 0