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31. If (G, .) is a group, such that (ab)2 =a2b2 ∀ a, b ∈ G, then G is a/an
commutative semi group
abelian group
non-abelian group
none of these
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32. (Z,*) is a group with a*b = a+b+1 ∀ a,b ∈ Z. The inverse of a is
0
-2
a-2
-a-2
33. Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an
subgroup
finite abelian group
infinite, non abelian group
infinite, abelian
34. Let A be the set of all non-singular matrices over real numbers and let * be the matrix multiplication operator. Then
A is closed under * but is not a semi group
is a semi group but not a monoid
is a monoid but not a group
is a group but not an abelian group
35. If a, b are positive integers, define a * b = α where ab = α (modulo 7), with this * operation, then inverse of 3 in group G (1, 2, 3, 4, 5, 6) is
3
1
5
4
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