Faithful irreducible representation of D8
= Faithful irreducible representation of D8
{c}
For $D_8=\langle r,s:r^4=s^2=1,\ srs=r^{-1}\rangle$, the matrices
$$
r\longmapsto
\begin{pmatrix}i&0\\0&-i\end{pmatrix},
\qquad
s\longmapsto
\begin{pmatrix}0&1\\1&0\end{pmatrix}
$$
define a faithful irreducible two-dimensional complex representation.