Left Coset by Identity

Theorem
Let $G$ be a group whose identity is $e$.

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

Then:
 * $e H = H$

where $e H$ is the left coset of $H$ by $e$.

Proof
We have:

So $e H = H$.

Also see
This is consistent with the definition of the concept of coset by means of the subset product:


 * $e H = \left\{{e}\right\} H$