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Set Theory and Algebra MCQ - Sets

31:  

If (G, .) is a group, such that (ab)2 =a2b2 ∀ a, b  ∈ G, then G is a/an

A.

commutative semi group

B.

abelian group

C.

non-abelian group

D.

none of these

 
 

Option: B

Explanation :

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32:  

 (Z,*) is a group with a*b = a+b+1 ∀ a,b ∈ Z. The inverse of a is

A.

0

B.

-2

C.

a-2

D.

-a-2

 
 

Option: D

Explanation :

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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

A.

subgroup

B.

finite abelian group

C.

infinite, non abelian group

D.

infinite, abelian

 
 

Option: C

Explanation :

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34:  

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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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

A.

3

B.

1

C.

5

D.

4

 
 

Option: C

Explanation :

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