The set of all real numbers under the usual multiplication operation is not a group since
A.  multiplication is not a binary operation 
B.  multiplication is not associative 
C.  identity element does not exist 
D.  zero has no inverse 
Option: D Explanation : 
If (G, .) is a group such that (ab) 1 = a1b1, ∀ a, b ∈ G, then G is a/an
A.  commutative semi group 
B.  abelian group 
C.  nonabelian group 
D.  None of these 

If (G, .) is a group such that a2 = e, ∀a ∈ G, then G is
A.  semi group 
B.  abelian group 
C.  nonabelian group 
D.  none of these 
Option: B Explanation : 