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51. The inverse of - i in the multiplicative group, {1, - 1, i , - i} is

1

-1

i

-i

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52. 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

53. In the group (G, .), the value of (a- 1 b)^{- 1} is

ab^{-1}

b^{- 1}a

a^{-1}b

ba^{-1}

54. If (G, .) is a group, such that (ab)^{2} = a^{2} b^{2} ∀ a, b ∈ G, then G is a/an

commutative semi group

abelian group

non-abelian group

none of these

55. (Z,*) is a group with a*b = a+b+1 ∀ a, b ∈Z. The inverse of a is

-2

a-2

-a-2

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