I would appreciate having a solution written with nice handwriting and detail explanations.

2. For each of the following sets of matrices, determine whether it is open, whether it is closed, and whether it is bounded. In fact, all these results generalize to n X n matrices. The following fact is useful: there are only two both open and closed sets in {4, the empty set and Q4 itself. (This holds for every R".) (a) The set of 2 X 2 symmetric matrices. (b) The set of 2 X 2 upper triangular matrices. (c) GLQCIR), the set of 2 X 2 invertible matrices. (d) SL2 (R), the set of 2 X 2 matrices with determinant equal to 1. (e) 02 (R), the set of 2 X 2 orthogonal matrices. (f) SO2( Q), the set of 2 X 2 orthogonal matrices with determinant equal to 1. 10 01 (g) 01,1( g) = {A E M2( Q) : ATBA = B}, where B = (h) The set of 2 X 2 row echelons