Left coset of some subgroup is right coset of other subgroup Let $G$ be a group. If a subset $A$ is a left coset of some subgroup of $G$, then show that $A$ is a right coset of some subgroup of $G$.

Let's say you take a subset $H$ of the group $G$.
Now, the a left coset of $H$ would particularly look like this:
$$aH = {{ ah | \forall h \in H}}$$
The inverse of the general element $ah$ is, $(ah)^{-1} = h^{-1}a^{-1}$. Every element in a group has an inverse, so you can safely say that any left coset is also a right coset.
