# How do you cube a matrix ([2, -1], [3, 1])?

Jul 30, 2018

The answer is $= \left(\begin{matrix}- 7 & - 4 \\ 12 & - 11\end{matrix}\right)$

#### Explanation:

If you have a matrix $A$

The cube is

$= {A}^{3} = {A}^{2} \cdot A$

Here,

$A = \left(\begin{matrix}2 & - 1 \\ 3 & 1\end{matrix}\right)$

Therefore,

${A}^{2} = A \cdot A = \left(\begin{matrix}2 & - 1 \\ 3 & 1\end{matrix}\right) \cdot \left(\begin{matrix}2 & - 1 \\ 3 & 1\end{matrix}\right)$

$= \left(\begin{matrix}1 & - 3 \\ 9 & - 2\end{matrix}\right)$

${A}^{3} = {A}^{2} \cdot A = \left(\begin{matrix}1 & - 3 \\ 9 & - 2\end{matrix}\right) \cdot \left(\begin{matrix}2 & - 1 \\ 3 & 1\end{matrix}\right)$

$= \left(\begin{matrix}- 7 & - 4 \\ 12 & - 11\end{matrix}\right)$