Did I do it right?

2. Let U be a subset of M1213 the vector space of 2X2 matrices with real number entries, where U is the set of all matrices of the form [3 2H] and a and b are real numbers. Identify which properties of a subspace are satised and not satised. Justify each claim with a proof or counterexample. 1. The zero matrix is in U, when a=0 and b=0. I] U D [3 2o b] = [0 2(0) {on} = [3 2. U is closed under vector addition given: set U, where m b are lall real numbers. Let T and V be matrices in set U. r=[: 2:11;] V=iy ny-y] I [g 2ohb]+[: Ely-yiziE; 2{a+x)bf{b+y)]l 3. U is closed under vector addition. I have already proven that the zero matrix is in U when a=b=0. If I let (1 be a scalar that is an}r real number then: dis 2.: bf] [bd Zad bd