Answer :

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

For, a, b ϵ N, we get,

a * b = a^{3} + b^{3} = b^{3} + a^{3} = b * a [Addition is commutative in N]

⇒ the operation * is commutative.

We can observed that (1*2)*3 = (1^{3}+2^{3})*3 = 9 * 3 = 93 + 33 = 729 + 27 = 756

Also, 1*(2*3) = 1*(2^{3} +3^{3}) = 1*(8 +27) = 1 × 35 = 1^{3} +35^{3} = 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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