If $E(\theta)=\begin{bmatrix}\cos^2\theta&\cos \theta\sin \theta\\\cos \theta\sin\theta&\sin^2\theta\end{bmatrix}$ and $\theta$ and $\phi$ differ by an odd multiple of $\large\frac{\pi}{2}$ then $E(\theta)E(\phi)$ is a

Question

$(a)\;unit\;vector\qquad(b)\;null\;matrix\qquad(c)\;diagonal\;matrix\qquad(d)\;None\;of\;these$