Question

State the reason for the following Binary Operation *, defined on the set Z of integers, to be not commutative : $a^{\ast }b=a{b}^3$

Answer 1

Note that $1^{\ast }2=1\times 2^3=8$ but $2^{\ast }1=2\times 1^3=2\ne 1^{\ast }2$ where 1,2 $ϵ$ Z. $\text{So* isn't commutative.}$