[tex] T = \left(\begin{array}{ccc}-1&-2&3\\2&4&6\\1&2&3\end{array}\right) \\ \\ T^2 = T\cdot T = \left(\begin{array}{ccc}-1&-2&-3\\2&4&6\\1&2&3\end{array}\right)\cdot \left(\begin{array}{ccc}-1&-2&-3\\2&4&6\\1&2&3\end{array}\right) = \\ \\ = \left(\begin{array}{ccc}-6&12&-18\\12&24&36\\6&12&18\end{array}\right) = 6 \cdot \left(\begin{array}{ccc}-1&-2&-3\\2&4&6\\1&2&3\end{array}\right) = \\ \\ = 6\cdot T\\ \\ \Rightarrow T^2 = 6^1 \cdot T\quad(1)\\ \\ \\T^3 = T^2\cdot T = (6\cdot T)\cdot T = 6\cdot T^2 = 6\cdot 6\cdot T = 6^2\cdot T\\ \\ \Rightarrow T^3 = 6^2\cdot T\quad (2)[/tex]
[tex]\text{Din (1) \c{s}i (2)}~\Rightarrow T^n = 6^{n-1}\cdot T = 6^{n-1}\cdot \left(\begin{array}{ccc}-1&-2&-3\\2&4&6\\1&2&3\end{array}\right) = \\ \\ \\\Rightarrow T^n = \left(\begin{array}{ccc}-6^{n-1}&\cdot -2\cdot 6^{n-1}&-3\cdot 6^{n-1}\\2\cdot 6^{n-1}&4\cdot 6^{n-1}&6\cdot 6^{n-1}\\1\cdot 6^{n-1}&2\cdot 6^{n-1}&3\cdot 6^{n-1}\end{array}\right) [/tex]
