Mon June 25, 2012 By: Arvindh Jambunathan

Q6.If a*b=3a+b on Z . check for commutativity & associativity.

Expert Reply
Tue June 26, 2012
answer : Given : a*b=3a+b on Z
  for commutativity : b*a = 3b+a which is not equal to 3a+b 
  therefore a*b is not equal to b*a 
hence it is not commutative.
for associativity :
(a*b) *c=  (3a+b)*c 
            =3(3a+b) +c =9a+3b+c ........(1)
a*(b*c)= a*(3b+c) 
             =3a+ 3b+c ....................(2)
since (1) is not equal to (2) , therefore its not associative.

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