$1\mapsto \left( \begin{array}{ccc} 1 & 0 \\ 0 & 1 \\ \end{array} \right)$

$i\mapsto \left( \begin{array}{ccc} \sqrt{-1} & 0 \\ 0 & \sqrt{-1} \\ \end{array} \right)$

$j\mapsto \left( \begin{array}{ccc} 0 & 1 \\ -1 & 0 \\ \end{array} \right)$

$k\mapsto \left( \begin{array}{ccc} 0 & \sqrt{-1} \\ \sqrt{-1} & 0 \\ \end{array} \right)$