The total number of matrices $A = \left( \begin{array} { c c c } 0 & 2 y & 1 \\ 2 x & y & - 1 \\ 2 x & - y & 1 \end{array} \right) , ( x , y \in R , x \neq y )$ for which $A ^ { T } A = 3 I _ { 3 }$ is: (1) 6 (2) 3 (3) 4 (4) 2
The total number of matrices $A = \left( \begin{array} { c c c } 0 & 2 y & 1 \\ 2 x & y & - 1 \\ 2 x & - y & 1 \end{array} \right) , ( x , y \in R , x \neq y )$ for which $A ^ { T } A = 3 I _ { 3 }$ is:\\
(1) 6\\
(2) 3\\
(3) 4\\
(4) 2