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1 . The set of all real numbers under the usual multiplication operation is not a group since
A. zero has no inverse
B. identity element does not exist
C. multiplication is not associative
D. multiplication is not a binary operation

2 . If (G, .) is a group such that (ab)- 1 = a-1b-1, ∀ a, b ∈ G, then G is a/an
A. commutative semi group
B. non-abelian group
C. abelian group
D. None of these

3 . If (G, .) is a group such that a2 = e, ∀a ∈ G, then G is
A. abelian group B. non-abelian group
C. semi group D. none of these

4 . The inverse of - i in the multiplicative group, {1, - 1, i , - i} is
A. -1 B. 1
C. -i D. i

5 . 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
A. -1 B. 0
C. 1 D. 2