Group/Inverse element/Unique/Fact/Proof

Proof

Let

${}x\circ y=y\circ x=e\,$

and

${}x\circ z=z\circ x=e\,.$

Then we have

${}y=y\circ e=y\circ (x\circ z)=(y\circ x)\circ z=e\circ z=z\,.$

To fact