Matrices and Determinants

Let $$x,y,z > 1$$ and A = \left[ {\matrix{ 1 & {{{\log }_x}y} & {{{\log }_x}z} \cr {{{\log }_y}x} & 2 & {{{\log }_y}z} \cr {{{\log }_z}x} & {{{\log }_z}y} & 3 \cr } } \right]. Then $$\mathrm{|adj~(adj~A^2)|}$$ is equal to