2. Which of the following are groups? For those which are not groups, explain why not (it is enough to find one axiom that fails). For those which are, state the identity and inverses: (i) Q under x, (ii) {q Q:q> 0} under ×, (iii) {q Q:q>0} under division, (iv) {1, 2, 3, 4, 5, 6, 7} under x mod 8, (v) {1,3,5, 7) under × mod 8, (vi) {2, 4, 6, 8, 10, 12} under x mod 14, a -b b a (vii) 2 x 2 real matrices of the form both 0, (viii) The set {0,1,2,3,4,5} under the operation roy = |x+y - 5. under matrix multiplication, with a and b not

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A: See attached file for a step by step explanation.

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