Question

Let * be a binary operation on Q,defined by a * b = 3ab 5. Show that * is commutative as well as associative.Also,find its identity, if it exists.

Answer 1

a*b=3ab

b*a=3ba

=3ab (since Q is commutative on multiple)

here a*b=b*a

so * is commutative

a*(b*c)=a*3bc

=9abc

=9bac

=9abc

=(a*b)*c

so * is commutative