Show that U(10)-->Z4 where f(3)=2. Show it's either an isomorphism or it isn't.

U(10) = {1,3,7,9} under multiplication and <3> with order 4.

Z4 is 0,1,2,3 under addition mod 4.

I know from a proposition in the book that U(10)-->Z4 is an isomorphism, but I can't quite figure out how f(3)=2 changes that.

Thanks.