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51. If (G, .) is a group such that a2 = e, ∀a ∈ G, then G is
semi group
abelian group
non-abelian group
none of these
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52. The inverse of - i in the multiplicative group, {1, - 1, i , - i} is
1
-1
i
-i
53. The set of integers Z with the binary operation "*" defined as a*b =a +b+ 1 for a, b ∈ Z, is a group. The identity element of this group is
0
12
54. In the group (G, .), the value of (a- 1 b)- 1 is
ab-1
b- 1a
a-1b
ba-1
55. If (G, .) is a group, such that (ab)2 = a2 b2 ∀ a, b ∈ G, then G is a/an
commutative semi group
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