If A=\begin{bmatrix}y&z&x\\ z&x&y\\ x&y&z\end{bmatrix} where x, y, z are integers, is an orthogonal matrix, then what is the value of x^{2}+y^{2}+z^{2}?

Explanation

For an orthogonal matrix, AA^T = I. The diagonal elements of AA^T represent the sum of the squares of the elements in the corresponding row of A. Therefore, the top-left element is y^2 + z^2 + x^2 = 1.

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