Hi, just working my way through the beginnings of some material for a group representations course I'll be taking next semester. The notes give an example of a representation of $\displaystyle S_3$ and I'm not quite sure how it's arrived at.

Let $\displaystyle \rho: S_3 \to GL_2\mathbb{C}$ be specified on the generators $\displaystyle (12)$ and $\displaystyle (123)$ by

$\displaystyle \rho_{(12)} =\begin{pmatrix}-1 & -1 \\0 & 1\\\end{pmatrix}$ and $\displaystyle \rho_{(123)} =\begin{pmatrix}-1 & -1 \\1 & 0\\\end{pmatrix}$

I'm just not entirely sure how these matrices are obtained, could anyone please enlighten me?

Thanks