Inverse of Subgroup

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Theorem

Let $\struct {G, \circ}$ 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.


Sources