for `x,x,z gt 0` Prove that `|{:(1,,log_(x)y,,log_(x)z),(log_(y)x,,1,,log_(y)z),(log_(z) x,,log_(z)y,,1):}| =0`

Explanation

To prove that the determinant of the given matrix is zero, we will follow these steps:

Given matrix:
\[
A = \begin{pmatrix}
1 & \log_x y & \log_x z \\
\log_y x & 1 & \log_y z \\
\log_z x & \log_z y & 1
...