Abelian Group Induces Entropic Structure

Theorem
Let $$\left({G, \circ}\right)$$ be an abelian group.

Let the operation $$*$$ be defined on $$G$$ such that:

$$\forall x, y \in G: x * y = x \circ y^{-1}$$

Then $$\left({G, *}\right)$$ is an entropic structure.