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The total number of matrices $A = \begin{pmatrix} 0 & 2y & 1 \ 2x & y & -1 \ 2x & -y & 1 \end{pmatrix}$, $(x, y \in \mathbb{R}, x \neq y)$ for which $A^T A = 3I_3$ is:
(1) $2$
(2) $3$
(3) $6$
(4) $4$
BETA
