Question

For the operation ∗ defined below, determine whether ∗ is binary, commutative or associative.

On Q, define a ∗ b = ab/2

Answer 1

commutative: a*b=ab/2=ba/2=b*a so a*b is commutative associative: (a*b)*c=ab*c/2=abc/2=a*bc=a*(b*c) so a*b is associative