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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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