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# If * is binary operation defined in N as a*b=$a^3+b^3$ then * is

Can you answer this question?

Toolbox:
• If a*b=b*a then * is commutative
• If (a*b)*c=a*(b*c) then * is associative
$a^3+b^3=b^3+a^3$ but $(a^3+b^3)^3+c^3\neq\:a^3+(b^3+c^3)^3$

$\Rightarrow\:$ * is commutative but not associative.

answered May 1, 2013