Inverse of Subgroup

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

Let $$H$$ be a subgroup of $$G$$.

Then:
 * $$H^{-1} = H$$

where $$H^{-1}$$ is the inverse of $$H$$.

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

The result follows.