The total number of matrices $$A = \left( {\matrix{ 0 & {2y} & 1 \cr {2x} & y & { - 1} \cr {2x} & { - y} & 1 \cr } } \right)$$ (x, y $ \in $ R,x $ \ne $ y) for which ATA = 3I3 is :-

Question

The total number of matrices
$$A = \left( {\matrix{ 0 & {2y} & 1 \cr {2x} & y & { - 1} \cr {2x} & { - y} & 1 \cr } } \right)$$
(x, y $ \in $ R,x $ \ne $ y) for which A^TA = 3I₃ is :-

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