Consider a binary operation * on N defined as a * b = a3 + b3, choose…

$a * b = b * a$

as $a^3+b^3=b^3+a^3$ (commutative true)

but $(a * b) * c = (a^3+b^3)^3+c^3$

$a *(b* c)=a^3+(b^3+c^3)^3$

so $(a * b) * c ≠ a *(b* c)$ (Not associative)