Question

If A = $\left[\begin{array}{ccc}1&1&3\\5&2&6\\-2&-1&-3\end{array}\right],$ then find A³

Answer 1

Answer:

$A^{3}=\left[\begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array}\right]$

Step-by-step explanation:

if  

$A^{3} =A^{2}\times A \\ \\A^{2}=\left[\begin{array}{ccc}1&1&3\\5&2&6\\-2&-1&-3\end{array}\right]\times\left[\begin{array}{ccc}1&1&3\\5&2&6\\-2&-1&-3\end{array}\right]\\\\\\A^{2}=\left[\begin{array}{ccc}0&0&0\\3&3&9\\-1&-1&-3\end{array}\right]$

so for

$A^{3} =A^{2}\times A \\\\=\left[\begin{array}{ccc}0&0&0\\3&3&9\\-1&-1&-3\end{array}\right] \times \left[\begin{array}{ccc}1&1&3\\5&2&6\\-2&-1&-3\end{array}\right]\\\\\\ =\left[\begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array}\right]\\\\\\=O$