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. 
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: (1:15am on Tuesday 26th 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: (11:49pm on Tuesday 27th June 2017)
Inverse : let a.(a2) = a (a2) 1= 1 = etherefore a inverse = a2 for all a belongs to Z

Let G denoted the set of all n x n nonsingular 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 : Click on Discuss to view users comments. 
Let A be the set of all nonsingular 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 : Click on Discuss to view users comments. 