If $A$ is a $3 \times 3$ matrix and $|A|=\frac{1}{2}$, then $\left|A^{-1}(\operatorname{Adj}(\operatorname{Adj} A))\right|^{-1}=$

Let $x=\alpha, y=\beta, z=\gamma$ be the unique solution of the system of simultaneous linear equations $2 x+3 y-2 z+4=0,3 x-4 y+3 z+5=0$, $k x-2 y+z+3=0$. If $\alpha=-2$, then $k=$

20. If $\frac{x^2+7}{\left(x^2+1\right)(x-2)}=\frac{A}{x-2}+\frac{B x+C}{x^2+1}$, then the determinant of the matrix $\left[\begin{array}{ll}A & B \\ C & \frac{2}{5}\end{array}\right]$ is