# How do you multiply [(4,-6),(2,-3)]^3?

Jul 3, 2016

$= \left[\begin{matrix}4 & - 6 \\ 2 & - 3\end{matrix}\right] \text{ }$ Interesting result!

#### Explanation:

${\left[\begin{matrix}4 & - 6 \\ 2 & - 3\end{matrix}\right]}^{3}$ means the same as ${x}^{3} \text{ ie } x \times x \times x$

=$\textcolor{red}{\left[\begin{matrix}4 & - 6 \\ 2 & - 3\end{matrix}\right] \times \left[\begin{matrix}4 & - 6 \\ 2 & - 3\end{matrix}\right]} \times \left[\begin{matrix}4 & - 6 \\ 2 & - 3\end{matrix}\right]$

First, multiply the first two matrices:

$\textcolor{red}{\left[\begin{matrix}4 & - 6 \\ 2 & - 3\end{matrix}\right]} \text{ surprising result!!}$

Now multiply by the third matrix

$\left[\begin{matrix}4 & - 6 \\ 2 & - 3\end{matrix}\right] \times \left[\begin{matrix}4 & - 6 \\ 2 & - 3\end{matrix}\right]$

$= \left[\begin{matrix}4 & - 6 \\ 2 & - 3\end{matrix}\right] \text{ I would not have guessed this one!}$