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6. In the group (G, .), the value of (a- 1 b)- 1 is
ab-1
b- 1a
a-1b
ba-1
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7. If (G, .) is a group, such that (ab)2 = a2 b2 ∀ a, b ∈ G, then G is a/an
commutative semi group
abelian group
non-abelian group
none of these
8. (Z,*) is a group with a*b = a+b+1 ∀ a, b ∈Z. The inverse of a is
0
-2
a-2
-a-2
9. 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
ininite, abelian
10. 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
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