This problem starts by using matrices as a model for complex numbers and showing that the structure 

$$ \left( \begin{array}{cc} 1& 0\\ 0& 1\end{array} \right)x+ \left( \begin{array}{cc} 0& -1\\ 1& 0\end{array} \right)y $$ behaves in the same way as $x+{\text i}y$.

The idea is then extended to introduce three different two by two matrices which all square to give $$ \left( \begin{array}{cc} -1& 0\\ 0& -1\end{array} \right) $$.At the end of the problem, there are some links and videos for further information about quaternions.

There are more matrix problems in this feature.