solve the following please

1. Let A = 9 3 . Find AT, A-1 , (A-1)T and ( AT ) -1. 2. Let A 2 1 and B - 8 (a) Find (AB)T, BT AT and ATBT. (b) (AB)-1, B-1A-1 and A-1B-1. 3. If B is the inverse of A2. Prove that (AB) is the inverse of A. 4. Prove or disprove that the following sets are subspaces of 2. (a) S = = T2 such that x1 = -2x2}. (b) S2 = fr = T 2 such that $1 = 0, 12 2 0}. (c) 53 = {x = such that 21 = 1}. 5. Prove or disprove that the following sets are subspaces of the space of 2 x 2 matrices. (a) S, is the set of 2 x 2 matrices A such that: 012 = a21 and a22 = 0. (b) S2 is the set of 2 x 2 matrices A such that: an1 + a22 = 0. (c) S3 is the set of nonsingular (invertible) 2 x 2 matrices. 6. Let A = and let b = (a) Find the rref(A). (b) Find the rank of A. (c) Find a such that b is in the column space of A