algebra, equivalence relation regarding associates

Question

If f(x) ~ g(x) if and only if f and g are associates, prove this is an equivalence relation

have tried to prove this both ways, struggling

Answer 1

Well you need to show 3 things :

1. Reflexivity : Take $u=1$
2. Symmetry : If $u$ works in one direction, then $u^{-1}$ works in the other.
3. Transitivity : If $f(x) = ug(x)$ and $g(x) = vh(x)$, then $f(x) = (uv)h(x)$, and $uv$ is a unit if $u$ and $v$ are.