Answer :

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

a b = ab2


We can see that for 2, 3 ϵ Q


2 * 3 = 2. 32 = 18 and 3 * 2 = 3. 22 = 12


2 * 3 ≠ 3 * 2


Therefore, the operation * is not commutative.


Also, 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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