If $D_1 = \begin{vmatrix}\frac{1}{2} & \frac{1}{\sqrt{2}} & 0\\-\frac{1}{\sqrt{2}} & \frac{1}{2} & 0 \\ 0 & 0 & 1\end{vmatrix} $ and $D_2=\begin{vmatrix}\frac{1}{\sqrt{2}}& \frac{1}{2} & 0\\\frac{-1}{2} & \frac{1}{\sqrt{2}}  & 0 \\ 0 & 0 & 1 \end{vmatrix}$, then $D_1D_2$ is equal to :

$\frac{9}{16}$

The correct answer is Option (3) → $\frac{9}{16}$

$D_1=1×\frac{1}{2}×\frac{1}{2}-\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{\sqrt{2}}\right)=\frac{1}{4}+\frac{1}{2}=\frac{3}{4}$

$D_1=\frac{3}{4}$

So $D_2=1×\left(\frac{1}{\sqrt{2}}×\frac{1}{\sqrt{2}}-\left(\frac{-1}{2}\right)×\left(\frac{1}{2}\right)\right)$

$D_2=\frac{3}{4}$

$⇒D_1D_2=\frac{9}{16}$