# Math Help - Prove * is commutative and associative

1. ## Prove * is commutative and associative

Assume that * is a binary operation on S with identity elements e and that x*(y*z)=(x*z)*y for all x,y,z E S. Prove * is commutative and associative!

2. Originally Posted by mandy123
Assume that * is a binary operation on S with identity elements e and that x*(y*z)=(x*z)*y for all x,y,z E S. Prove * is commutative and associative!
If you let $x=e$ then $e(yz) = (ez)y \implies yz = zy$. This is commutative.

Now $x(yz) = (xz)y \implies x(zy) = (xz)y$. This is associate.