non-trivial-solution

If the following system has non - trivial solution $$$px+qy+rz=0$$$ $$$qx+ry+pz=0$$$ $$$rx+py+qz=0$$$ Then which one of the following Options is TRUE ?

$$A$$ system of equations represented by $$AX=0$$ where $$X$$ is a column vector of unknown and $$A$$ is a square matrix containing coefficients has a non-trival solution when $$A$...