Please solve this and explain the answer to me. please do not use cursive as I can't read it.

1. Let A = 2 1 4 3 Find AT, A-1, (A-1)T and (AT)-1. 2. Let A = -2 2 ] and B = [3 -3] (a) Find (AB) T, BT AT and ATBT. (b) (AB) -1, B-lA- and A-1B-1. 3. By trial and error, find a 2 x 2 nonzero matrix A such that A? = 0. 4. Prove or disprove that the following sets are subspaces of R2. (a) Si = {x = T1 such that x1 = 5x2}. (b) S2 = fx = T1 such that 1 2 0,x2 2 0}. (c) S3 = {x = T1 such that x1 = =2 +1}