Question

If $A=\left[\begin{array}{ccc}3& 0& 0\\ 0& 3& 0\\ 0& 0& 3\end{array}\right]$ then find $A^4$.

Answer 1

$\begin{array}{c}A=\left(\begin{array}{ccc}3& 0& 0\\ 0& 3& 0\\ 0& 0& 3\end{array}\right)\\ A=\left(\begin{array}{ccc}{3}^4& 0& 0\\ 0& 3^4& 0\\ 0& 0& 3^4\end{array}\right)=\left(\begin{array}{ccc}81& 0& 0\\ 0& 81& 0\\ 0& 0& 81\end{array}\right)\end{array}$