(chatquestion)...Mathematics 36. 2074 Supp Q.No. 5b OR Let G be a group. If a, be(G 421 prove that (a*b) 1 = b¯1 *a1. 37. 2074 Set A Q.No. 6a If a and b are the elements of o 207 (G,"), and If a* b = e, prove that b = a ii.If a* b =b, prove that a = e. 38. 2074 Set B Q.No. 5b Show that {2", n e z) is an Abelian group with respect to multiplication. 39. 2074 SetB Q.No. 5b OR If a, b e (G, o) where G is a groun Prove that: i. (aob)-1 = b-1 o a! 40. 2073 Supp Q.No. 5b Define abelian group. If (G, ") is a abelian group, show that (a*b)-1 = a-1*b-'; a, beG. 41. 2073 Supp Q.No. 5b OR Verify that {2m : me Z) is abelian group with respect to multiplication, where Z is set of intègers. i. (a)1 = a. 2. 2073 Set C Q.No. 5b Define Abelian group. Prove group G is Abelian if and only if (a o b)1 = at o b' fo- beG. 2073 Set C Q.No. 5b OR Show that the set of all omposition defim...(No. 38)

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