Detritivores, such as earthworms, feed on decomposing organic matter and help in nutrient recycling by breaking down dead and decaying plant and animal material.
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]