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 
Option: C Explanation : Click on Discuss to view users comments. 
In the group (G, .), the value of (a 1 b) 1 is
A.  ab^{1} 
B.  b^{ 1}a 
C.  a^{1}b 
D.  ba^{1} 
Option: B Explanation : Click on Discuss to view users comments. 
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 : Click on Discuss to view users comments. 
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.  nonabelian group 
D.  none of these 
Option: B Explanation : Click on Discuss to view users comments. 
(Z,*) is a group with a*b = a+b+1 ∀ a, b ∈Z. The inverse of a is
A.  0 
B.  2 
C.  a2 
D.  a2 
Option: D Explanation : Click on Discuss to view users comments. sachin kushare said: (6:15pm 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=2aso correct option (D)
Simran said: (4:49pm on Tuesday 27th June 2017)
Inverse : let a.(a2) = a (a2) 1= 1 = etherefore a inverse = a2 for all a belongs to Z
