Theorem: for any positive integer n, is isomorphic to .

Q: Prove that every element is determined by ; meaning, results in a well-defined automorphism of .

A: let be arbitrary. Then is an isomorphism. So, to show if something is well-defined I need to show if a=c, b=d, then a*b=c*d. I am not sure what to my a,b, and c's are. I know . so, do I let and . Now, I want to show ?

Thanks