ابتدا ${A^2}$ را به دست می‌آوریم.

${A^2} = \left[ {\begin{array}{*{20}{c}}3\\2\\0\end{array}\,\,\,\begin{array}{*{20}{c}}{ - 3}\\{ - 3}\\1\end{array}\,\,\,\begin{array}{*{20}{c}}4\\4\\1\end{array}} \right]\left[ {\begin{array}{*{20}{c}}3\\2\\0\end{array}\,\,\,\begin{array}{*{20}{c}}{ - 3}\\{ - 3}\\{ - 1}\end{array}\,\,\,\begin{array}{*{20}{c}}4\\4\\1\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}3\\0\\{ - 2}\end{array}\,\,\begin{array}{*{20}{c}}{ - 4}\\{ - 1}\\2\end{array}\,\,\begin{array}{*{20}{c}}4\\0\\{ - 3}\end{array}} \right]$

کافی است سطر اول ${A^2}$ را در ${A^2}$ ضرب کنیم تا سطر اول ${A^4}$ مشخص شود.

${A^4} = \left[ {\begin{array}{*{20}{c}}3\\0\\{ - 2}\end{array}\,\,\begin{array}{*{20}{c}}{ - 4}\\{ - 1}\\2\end{array}\,\,\begin{array}{*{20}{c}}4\\0\\{ - 3}\end{array}} \right]\left[ {\begin{array}{*{20}{c}}3\\0\\{ - 2}\end{array}\,\,\begin{array}{*{20}{c}}{ - 4}\\{ - 1}\\2\end{array}\,\,\begin{array}{*{20}{c}}4\\0\\{ - 3}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&0&0\end{array}} \right]$