Answer :

It is given that be a binary operation on the set Q of rational numbers is defined as

a b = a2 + b2


For a, b ϵ Q, we get,


a * b = a2 + b2 = b2 + a2 = b * a


the operation is commutative.


We can see that (1 * 2) * 3 ≠ 1 *(2 * 3), where 1,2,3 ϵ Q


Therefore, the operation * is not associative.


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