3. Let A, B be two nonsingular n x n matrices and let C be a matrix of order n such that A'lB = CA. Is C nonsingular, and if so, nd 0'1? 4. Prove or disprove that the following sets are subspaces of R2. (a) 51 = {z = [ 2:1 ] such that 1:1 = 31'2}. (b) 52 = {z = [ x1 ] such that 1:2 = 0,251 2 0}. (c) 53 ={17 = [ \"1 ] such that 1:1 = 0}. 5. Prove or disprove that the following sets are subspaces of the space of 2 X 2 matrices. (a) 51 is the set of 2 x 2 matrices A such that: an 2 a21 and an 2 can. (b) 32 is the set of 2 x 2 matrices A such that: all + (122 = 1. (c) 53 is the set of singular (noninvertible) 2 x 2 matrices