Associate of twisted subgroup is twisted subgroup

Statement
Suppose $$K$$ is a twisted subgroup inside a group $$G$$. Suppose $$a \in K$$. Then, the following are true:


 * $$Ka = a^{-1}K$$.
 * $$Ka$$ is a twisted subgroup of $$G$$.

We say that $$Ka$$ is an associate of $$K$$.