If $A=\left[\begin{array}{ccc}k & 5 & 2 \\ 2 & -k & 5 \\ 5 & 2 & -k\end{array}\right]$ and $\operatorname{det} A=190$, then $\operatorname{adj} A=$

If the unique solution of the simultaneous linear equations $3 x-2 y+z=5 k, 2 x+3 y-2 z=-5 k$, $x+4 y+3 z=k$ is $x=\alpha, y=\beta, z=3$, then $k=$

$$ \left|\begin{array}{ccc} \sqrt{3} & 2 \sqrt{5} & \sqrt{5} \\ \sqrt{15} & 5 & \sqrt{10} \\ 3 & \sqrt{15} & 5 \end{array}\right|= $$

If $A$ is a non-singular matrix such that $(A-2 I)$ $(A-3 I)=0$, then $\frac{1}{5} A+\frac{6}{5} A^{-1}=$