Let $\mathrm{A}=\left[\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right]\mathrm{ }$ . The only correct statement about matrix $\mathrm{A}\mathrm{ }$ is

If the system of equations

$x+4 a y+a z=0$

$x+3 b y+b z=0$

$x+2 c y+c z=0$
have a nonzero solution, then $a,b,c(\ne 0)$ are in

If $a\ne b\ne c,$ then one value of $x$ which satisfies the equation

$\left|\begin{array}{ccc}0& x-a& x-b\\ x+a& 0& x-c\\ x+b& x+c& 0\end{array}\right|=0$ is given by