Question

If $A=\left[\begin{array}{cc}1& 2\\ 3& -1\end{array}\right]\mathrm{and}B=\left[\begin{array}{cc}1& -4\\ 3& -2\end{array}\right],\mathrm{find}\left|AB\right|$.

Answer 1

$$\begin{gathered} A=\left[\begin{array}{cc}1& 2\\ 3& -1\end{array}\right] \\ \Rightarrow \left|A\right|=-1-6=-7 \\ B=\left[\begin{array}{cc}1& -4\\ 3& -2\end{array}\right] \\ \Rightarrow \left|B\right|=-2+12=10 \\ \mathrm{If}A\mathrm{and}B\mathrm{are}\mathrm{square}\mathrm{matrices}\mathrm{of}\mathrm{the}\mathrm{same}\mathrm{order},\mathrm{then}\left|AB\right|=\left|A\right|\left|B\right|. \\ \Rightarrow \left|AB\right|=\left|A\right|\left|B\right|=-7\times 10=-70 \end{gathered}$$