Answer :

On N, the operation * is defined as a * b = a3 + b3

For, a, b ϵ N, we get,


a * b = a3 + b3 = b3 + a3 = b * a [Addition is commutative in N]


the operation * is commutative.


We can observed that (1*2)*3 = (13+23)*3 = 9 * 3 = 93 + 33 = 729 + 27 = 756


Also, 1*(2*3) = 1*(23 +33) = 1*(8 +27) = 1 × 35 = 13 +353 = 1 + (35)3 = 1 + 42875 = 42876.


Therefore, (1 * 2)*3 1*(2*3); where 1,2,3 ϵ N


Therefore, the operation * is not associative.


Therefore, the operation * is commutative, but not associative.

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