Vc pediu algo bem trabalhoso, hein! Se não colocar como a melhor resposta... é muita ingratidão!
Vamos lá:
[tex]X:\left[\begin{array}{ccc}-1&-2&4\\-1&1&0\\0&2&3\end{array}\right] .Y:\left[\begin{array}{ccc}a&d&g\\b&e&h\\c&f&i\end{array}\right] =Z:\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\\ (Determinante)=>|X|=-17\\ X^{-1}:\left[\begin{array}{ccc}\frac{|Ya|}{|X|}&\frac{|Yd|}{|X|}&\frac{|Yg|}{|X|}\\\frac{|Yb|}{|X|}&\frac{|Ye|}{|X|}&\frac{|Yh|}{|X|}\\\frac{|Yc|}{|X|}&\frac{|Yf|}{|X|}&\frac{|Yi|}{|X|}\end{array}\right]\\Ya\left[\begin{array}{ccc}1&-2&4\\0&1&0\\0&2&3\end{array}\right]\\=>|Ya|=3\\ [/tex]
[tex] Yb\left[\begin{array}{ccc}-1&1&4\\-1&0&0\\0&0&3\end{array}\right]\\=>|Yb|=3\\ Yc\left[\begin{array}{ccc}-1&-2&1\\-1&1&0\\0&2&0\end{array}\right]\\=>|Yc|=-2\\ Yd\left[\begin{array}{ccc}0&-2&4\\1&1&0\\0&2&3\end{array}\right]\\=>|Yd|=14\\ Ye\left[\begin{array}{ccc}-1&0&4\\-1&1&0\\0&0&3\end{array}\right]\\=>|Ye|=-3\\ Yf\left[\begin{array}{ccc}-1&-2&0\\-1&1&1\\0&2&0\end{array}\right]\\=>|Yf|=2\\ [/tex]
[tex]Yg\left[\begin{array}{ccc}0&-2&4\\0&1&0\\1&2&3\end{array}\right]\\=>|Yg|=-4\\ Yh\left[\begin{array}{ccc}-1&0&4\\-1&0&0\\0&1&3\end{array}\right]\\=>|Yh|=-4\\ Yi\left[\begin{array}{ccc}-1&-2&0\\-1&1&0\\0&2&1\end{array}\right]\\=>|Yi|=-3\\ X^{-1}: \left[\begin{array}{ccc}\frac{3}{-17}&\frac{14}{-17}&\frac{4}{17}\\\frac{3}{-17}&\frac{3}{17}&\frac{4}{17}\\\frac{2}{17}&\frac{2}{-17}&\frac{3}{17}\end{array}\right]\\ [/tex]
