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Set Theory and Algebra MCQ - Algebra

11:  

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

A.

subgroup

B.

finite abelian group

C.

infinite, non abelian group

D.

ininite, abelian

 
 

Option: C

Explanation :

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12:  

Let A be the set of all non-singular matrices over real numbers and let * be the matrix multiplication operator. Then

A.

A is closed under * but < A, * > is not a semi group

B.

< A, * > is a semi group but not a monoid

C.

< A, * > is a monoid but not a group

D.

< A, * > is a group but not an abelian group

 
 

Option: D

Explanation :

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13:  

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

A.

3

B.

1

C.

5

D.

4

 
 

Option: C

Explanation :

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14:  

Which of the following is TRUE ?

A.

Set of all rational negative numbers forms a group under multiplication

B.

Set of all non-singular matrices forms a group under multiplication

C.

Set of all matrices forms a group under multipication

D.

Both (b) and (c)

 
 

Option: B

Explanation :

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15:  

The set of all nth roots of unity under multiplication of complex numbers form a/an

A.

semi group with identity

B.

commutative semigroups with identity

C.

group

D.

abelian group

 
 

Option: D

Explanation :

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