$\LARGE M^{-1}$ = Inverse Mtrix of M = $\LARGE \frac{1}{det(M)}adj(M)$

Got it !

Inverse matrix of a 3 x 3 matrix

$ \LARGE \begin{bmatrix} \color{black}1 & \color{black}2 & \color{black}-1 \\\color{black}2 &\color{black}1&\color{black}2\\\color{black}-1 &\color{black}2&\color{black}1 \end{bmatrix}^{-1} = $	$ \LARGE \frac{1}{-16} \begin{bmatrix} \color{black}-3 & \color{black}-4 & \color{black}5 \\\color{black}-4 &\color{black}0&\color{black}-4\\\color{black}5 &\color{black}-4&\color{black}-3 \end{bmatrix} = $ $ \LARGE \begin{bmatrix} \color{black}\frac{3}{16} & \color{black}\frac{1}{4} & \color{black}\frac{-5}{16} \\\color{black}\frac{1}{4} &\color{black}0&\color{black}\frac{1}{4}\\\color{black}\frac{-5}{16} &\color{black}\frac{1}{4}&\color{black}\frac{3}{16} \end{bmatrix}$
$ \LARGE \begin{bmatrix} \color{black}1 & \color{black}2 & \color{black}3 \\\color{black}0 &\color{black}4&\color{black}5\\\color{black}0 &\color{black}0&\color{black}6 \end{bmatrix}^{-1} = $	$ \LARGE \frac{1}{24} \begin{bmatrix} \color{black}24 & \color{black}-12 & \color{black}-2 \\\color{black}0 &\color{black}6&\color{black}-5\\\color{black}0 &\color{black}0&\color{black}4 \end{bmatrix} =$ $ \LARGE \begin{bmatrix} \color{black}1 & \color{black}-\frac{1}{2} & \color{black}-\frac{1}{12} \\\color{black}0 &\color{black}\frac{1}{4}&\color{black}-\frac{5}{24}\\\color{black}0 &\color{black}0&\color{black}\frac{1}{6} \end{bmatrix}$
$ \LARGE \begin{bmatrix} \color{black}1 & \color{black}0 & \color{black}0 \\\color{black}0 &\color{black}1&\color{black}0\\\color{black}0 &\color{black}0&\color{black}1 \end{bmatrix}^{-1} = $	$ \LARGE \frac{1}{1} \begin{bmatrix} \color{black}1 & \color{black}0 & \color{black}0 \\\color{black}0 &\color{black}1&\color{black}0\\\color{black}0 &\color{black}0&\color{black}1 \end{bmatrix} = $ $ \LARGE \begin{bmatrix} \color{black}1 & \color{black}0 & \color{black}0 \\\color{black}0 &\color{black}1&\color{black}0\\\color{black}0 &\color{black}0&\color{black}1 \end{bmatrix} $
$ \LARGE \begin{bmatrix} \color{black}1 & \color{black}2 & \color{black}3 \\\color{black}0 &\color{black}4&\color{black}5\\\color{black}0 &\color{black}0&\color{black}0 \end{bmatrix}^{-1} = $	does not exist, because $det(M = 0$)