For positive numbers $x,y$ and $z$ the numerical value of the determinant $\begin{vmatrix}1 &\log_xy&\log_xz\\\log_yx&1&\log_yz\\\log_zx&\log_zy&1\end{vmatrix}$ is

Question

$(a)\;1\qquad(b)\;0\qquad(c)\;2\qquad(d)\;3$