The total number of matrices \(A = \left[ {\begin{array}{*{20}{c}}0&{2{\rm{y}}}&1\\{2{\rm{x}}}&{\rm{y}}&{ - 1}\\{2{\rm{x}}}&{ - {\rm{y}}}&1\end{array}} \right],\left( {{\rm{x}},{\rm{y}} \in \rm{R},{\rm{x}} \ne \rm{}{\rm{y}}} \right)\) for which \({{\rm{A}}^{\rm{T}}}{\rm{A}} = 3{{\rm{I}}_3}{\rm{\;}}\) is:

• A. 2
• B. 3
• C. 6
• D. 4