Let M denote the group of 2 x 2 non-singular real matrices under multiplication. Let O denote the subgroup of orthogonal matrices (i.e., A-1 = A") in M. a. Show O decomposes as the disjoint union of...

Extracted text: Let M denote the group of 2 x 2 non-singular real matrices under multiplication. Let O denote the subgroup of orthogonal matrices (i.e., A-1 = A") in M. a. Show O decomposes as the disjoint union of 0+ = { A e 0 |Det(A) = 1} and 0- = { A e 0 ||Det(A) = –1}. b. Is O+ a normal subgroup of O? Is 0¯? c. Is O+ a normal subgroup of M?