I need to show that f(x)=x^3 is an automorphism of U(16) ie.(adsbygoogle = window.adsbygoogle || []).push({});

{1,3,5,7,9,11,13,15} with operation (multiplication)mod 16. I am having trouble showing that f is 1 to 1. I know it is 1 to 1 because I took each element calculated it to make sure, but how do I show that it is 1 to 1. I would usually assume f(a)=f(b) then show a = b but im stuck there. Once I show its 1 to 1 im pretty much done because its guaranteed to be onto since U(16) is finite.

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# U(16) automorphism

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