# Set Theory and Algebra MCQ - Algebra

6:

The set of integers Z with the binary operation "*" 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 Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
7:

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

 A. ab-1 B. b- 1a C. a-1b D. ba-1 Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
8:

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) Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
9:

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 Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
10:

(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 Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. sachin kushare said: (4:15pm on Monday 25th February 2013) we have a*e=a....(Identity property)so, a e 1=aso, e=-1we have a*b=-1....(Inverse property)so, a b 1=-1 b=-2-aso correct option (D) Simran said: (1:49pm on Tuesday 27th June 2017) Inverse : let a.(-a-2) = a (-a-2) 1= -1 = etherefore a inverse = -a-2 for all a belongs to Z Write your comments here:

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