Classical

Set Theory and Algebra MCQ - Algebra

6:  

 In the group (G, .), the value of (a- 1 b)- 1 is

A.

ab-1

B.

b- 1a

C.

a-1b

D.

ba-1

 
 

Option: B

Explanation :


7:  

If (G, .) is a group, such that (ab)2 = a2 b2 ∀ 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 :


8:  

 (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 :


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

A.

subgroup

B.

finite abelian group

C.

infinite, non abelian group

D.

ininite, abelian

 
 

Option: C

Explanation :


10:  

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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