Given that $$\int_{-\infty}^\infty e^{{-x}^2} dx = \sqrt{\pi}$$ The value of: $$\iint_{-\infty}^\infty e^{{{-(x}^2}+xy+{{y}^2)}}dxdy$$ is A) $\sqrt{\frac{\pi}{3}}$ B)$\frac{\pi}{\sqrt3}$ C)$\sqrt{\frac{2\pi}{3}}$ D)$\frac{2\pi}{\sqrt3}$
*Both the limits of double integral is from $-\infty$ to $\infty$ *
I tried with integration by parts and it is leading nowhere.Please help.
