let $(B,\star)$ defines a monoid with a finite number of elements Let. the elements of $B$ be $\{x_1,x_2,x_3,x_4,\cdots\}$ where every element of $B$ occurs exactly once in this list
let $y$ be the invertible element of the monoid.
Prove that every element of the monoid occurs exactly once in this list $\{ y\star x_1,y \star x_2, \cdots, y\star x_n \}$.
Can anyone please point me in the right direction where to start? without telling me the answer.