$ \Rightarrow \left[ {\begin{array}{*{20}{c}}
0&{2x}&{2x}\\
{2y}&y&{ - y}\\
1&{ - 1}&1
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
0&{2y}&1\\
{2x}&y&{ - 1}\\
{2x}&{ - y}&1
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
3&0&0\\
0&3&0\\
0&0&3
\end{array}} \right]$

$ \Rightarrow \left[ {\begin{array}{*{20}{c}}
{8{x^2}}&0&0\\
0&{6{y^2}}&0\\
0&0&3
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
3&0&0\\
0&3&0\\
0&0&3
\end{array}} \right]$

$ \Rightarrow 8{x^2} = 3 \Rightarrow x =  \pm \sqrt {\frac{3}{8}} $

$ \Rightarrow 6{y^2} = 3 \Rightarrow y =  \pm \sqrt {\frac{1}{2}} $

$4$ matrices are possible