I need to prove that there is one homomorphism $\varphi : Dn \to Sn$ such that

Question

I need to prove that there is one homomorphism $\varphi : Dn \to Sn$ such that

$\varphi$($\tau$) =

$$ \begin{pmatrix} 1 & 2 & . & .& . & n \\ 2 & 3 & . & .& . & 1 \\ \end{pmatrix} $$

$\varphi$($\sigma$) =

$$ \begin{pmatrix} 1 & 2 & 3 & .& n-1 & n \\ 1 & n & n-1 & .& 3 & 2 \\ \end{pmatrix} $$

I understand that each number is a vertex and that tau means a turn one vertex to the right taking each number to the next and sigma is a mirror. beside that I don't really understand what is the question. any help will be aprriciated