Jawaharlal Nehru Port (Nhava Sheva) is a significant seaport in Maharashtra. Located near Mumbai, it is the busiest container port in India and plays a crucial role in the country’s international trade. The port handles a significant portion of India’s cargo, facilitating imports and exports. Its strategic location and extensive infrastructure make it a vital node in India’s maritime trade.
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]