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 $|\operatorname{adj}|\left(A^2\right) \mid=$

If the system of simultaneous linear equations $x-2 y+z=0,2 x+3 y+z=6$ and $x+2 y+p z=q$ has infinitely many solutions, then

If the system of linear equations $(\sin \theta) x-y+z=0$, $x-(\cos \theta) y+z=0, x+y+(\sin \theta) z=0$ has non-trivial solution, then the least positive value of $\theta$ is