The number of real values of ' $a$ ' for which the system of equations $2 x+3 y+a z=0, x+a y-2 z=0$ and $3 x+y+3 z=0$ has non-trivial solution is

If $x=\alpha, y=\beta, z=\gamma$ is the solution of the system of equations $2 x+3 y+z=-1,3 x+y+z=4$, $x-3 y-2 z=1$, then the value of $\beta$ is

The positive value of ' $a$ ' for which the system of linear homogeneous equations $x+a y+z=0, a x+2 y-z=0$, $2 x+3 y+z=0$ has non-trivial solution is

If $A=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 1 \\ 1 & 2 & 1\end{array}\right]$ then $|\operatorname{adj}|\left(A^2\right) \mid=$