Durban is a significant seaport in South Africa. Located on the eastern coast, it is one of the busiest and most important ports in Africa. Durban handles a wide variety of goods, including oil, coal, and agricultural products, and is a major hub for international trade. The port plays a critical role in South Africa’s economy, facilitating imports and exports, particularly to and from the Indian Ocean region.
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]