Classical

Set Theory and Algebra MCQ - Sets

26:  

The inverse of - i in the multiplicative group,{1, - 1,i,- i } is

A.

1

B.

-1

C.

i

D.

-i

 
 

Option: C

Explanation :


27:  

The set of integers Z with the binary operation "1" defined as a*b =a +b+1 for a, b ∈ Z, is a group. The identity element of this group is

A.

0

B.

1

C.

-1

D.

12

 
 

Option: C

Explanation :


28:  

 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 :


29:  

revise 114. The identity element in the group
G={[x x]}:x €R,x#0} with respect to matrix
     {[x x]}
multiplication is

A.

(1/0 0/1)

B.

(-1/0 0/-1)

C.

((1/2)/(1/2) (1/2)/(1/2))

D.

(1/1 1/1)

 
 

Option: C

Explanation :


30:  

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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