[tex]\begin{vmatrix}m+2 & m & m \\ m & m+2 & m \\ m & m & m+2\notag\end{vmatrix} =\begin{vmatrix}3m+2 & 3m+2 & 3m+2 \\ m & m+2 & m \\ m & m & m+2\notag\end{vmatrix} = \\\\\\(3m+2)\begin{vmatrix}1 & 1 & 1 \\ m & m+2 & m \\ m & m & m+2\notag\end{vmatrix} = (3m+2)\begin{vmatrix}1 & 0 & 0 \\ m & 2 & 0 \\ m & 0 & 2\notag\end{vmatrix} =\\ \\=(3m+2)(4) = 12m+8[/tex]
[tex]A^{-1} = \frac{1}{det(A)}*A^*\\ A^{-1}=A^* \implies det(A)=1\\12m+8=1\\12m=-7\\m=\frac{-7}{12}[/tex]
