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

Explanation

Matrix A is symmetric by its definition, so A = A^T. Given A is orthogonal, we know A A^T = I. Substituting A^T with A yields A A = A^2 = I, which is the Identity matrix.

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