JEE Math Practice Question

If $$A = \left( {\begin{matrix} 0 & {\sin \alpha } \\ {\sin \alpha } & 0 \\ \end{matrix} } \right)$$ and $$\det \left( {{A^2} - {1 \over 2}I} \right) = 0$$, then a possible value of $$\alpha$$ is :

1. A.$${\pi \over 4}$$
2. B.$${\pi \over 6}$$
3. C.$${\pi \over 2}$$
4. D.$${\pi \over 3}$$