$\text{ Let }A=\left[\begin{array}{cc}i& -i\\ -i& i\end{array}\right],i=\sqrt{-1}\text{ then the system of linear equations }{A}^8\left[\begin{array}{l}x\\ y\end{array}\right]=\left[\begin{array}{l}8\\ 64\end{array}\right]\text{ has }$

$\begin{array}{l}{A}^2=\left[\begin{array}{cc}i& -i\\ -i& i\end{array}\right]\left[\begin{array}{cc}i& -i\\ -i& i\end{array}\right]=\left[\begin{array}{cc}-2& 2\\ 2& -2\end{array}\right]\text{\hspace{0.17em} and }{A}^4=\left[\begin{array}{cc}8& -8\\ -8& 8\end{array}\right];A^8=\left[\begin{array}{cc}128& -128\\ -128& 128\end{array}\right]\\ \text{Hence the equations are 128}\left(x-y\right)=8\text{\hspace{0.17em}\hspace{0.17em}and 128}\left(-x+y\right)=64\\ \text{No solution.}\end{array}$