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Math Help - Prove * is commutative and associative

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    Unhappy 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!
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    Quote Originally Posted by mandy123 View Post
    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.
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