The Amazon River is an important river in South America. It is the longest river by discharge of water in the world and plays a critical role in the ecosystem of the Amazon Rainforest. The river is central to transportation, trade, and agriculture in the region. It also supports a vast array of biodiversity and influences global climate patterns
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]