Question
Mon June 25, 2012 By: Arvindh Jambunathan
 

Q5. Find identity element for a*b=a+b+1 in Z.

Expert Reply
Tue June 26, 2012
Given : a*b=a+b+1 in Z
 
Let e be the identity element in Z for the binary operator * on Z . 
 
then , 
 
a*e=a =e*a for all a belongs to Z
 
a*e=a and e*a =a  for all a belongs to Z
 a+e+1 =a  and e+a+1 =a
 
hence e= -1                               
 
e= - 1 is the identity element in Z 
   
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