If $A = \left[ \begin{array} { c c } 0 & \sin \alpha \\ \sin \alpha & 0 \end{array} \right]$ and $\operatorname { det } \left( A ^ { 2 } - \frac { 1 } { 2 } \mathrm { I } \right) = 0$, then a possible value of $\alpha$ is\\
(1) $\frac { \pi } { 2 }$\\
(2) $\frac { \pi } { 3 }$\\
(3) $\frac { \pi } { 4 }$\\
(4) $\frac { \pi } { 6 }$