Find the value of $x, y, z $ if the matrix. $\begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix}$ satisfy the equation $A^TA =I_3$

Question

$(A)\;x = \pm \frac{1}{\sqrt 2} , y = \pm \frac{1}{\sqrt 6} , z = \pm \frac{1}{\sqrt 3}$
$(B)\;x = \pm \frac{1}{\sqrt 3} , y = \pm \frac{1}{\sqrt 2} , z = \pm \frac{1}{\sqrt 6}$
$(C)\;x = \pm \frac{1}{2} , y = \pm \frac{1}{ 6} , z = \pm \frac{1}{3}$
$(D)\; x = \pm \frac{1}{3} , y = \pm \frac{1}{2} , z = \pm \frac{1}{6}$