"Let $x,y$ be elements of the group G. Prove the following is an equivalence relation: $x$ is related to $y$ iff there exists some $g$ in $G$ such that $y = g \cdot x \cdot g^{-1}$"
Now I understand that I must prove that the relation is reflexive,symmetric and transitive. But without knowledge of the set or whether the group binary operation is commutative I'm getting very confused on how to do it. I know that I just need to use the group properties of associativity, closure invertibility and identity, but I'm unsure how.
Any help appreciated.