Inverse of Subgroup

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

Then $$\forall H \le \left({G, \circ}\right): H^{-1} = H$$

Proof
As $$H$$ is a subgroup of $$G$$, $$\forall h \in H: h^{-1} \in H$$.

The result follows.