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56. 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
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57. 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
58. If a, b are positive integers, define a * b = a where ab = a (modulo 7), with this * operation, then inverse of 3 in group G (1, 2, 3, 4, 5, 6) is
3
1
5
4
59. Which of the following is TRUE ?
Set of all rational negative numbers forms a group under multiplication
Set of all non-singular matrices forms a group under multiplication
Set of all matrices forms a group under multiplication
Both (b) and (c)
60. The set of all nth roots of unity under multiplication of complex numbers form a/an
semi group with identity
commutative semigroups with identity
group
abelian group
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