Question

If $A=\left[\begin{array}{cc}1& 2\\ 3& -1\end{array}\right]\mathrm{and}B=\left[\begin{array}{cc}1& 0\\ -1& 0\end{array}\right]$, find |AB|.

Answer 1

$$\begin{gathered} A=\left[12 \\ 3-1\right] \\ B=\left[10 \\ -10\right] \\ AB=\left[12 \\ 3-1\right]\left[10 \\ -10\right]=\left[\begin{array}{cc}1-2& 0+0\\ 3+1& 0+0\end{array}\right]=\left[\begin{array}{cc}-1& 0\\ 4& 0\end{array}\right] \\ \left|AB\right|=0-0=0 \end{gathered}$$