Well, we were told "Be fruitful and multiply"!
(Sorry, I couldn't help myself!)
The set of 2 by 2 matrices forms a vector space with scalar multiplication defined by $\displaystyle u\begin{bmatrix}a & b \\ c & d\end{bmatrix}= \begin{bmatrix} ua & ub \\ uc & ud\end{bmatrix}$.