2. Given that the equations of the two asymptotes of a hyperbola are $x-\sqrt{3} y=0$ and $\sqrt{3} x+y=0$, then its eccentricity is ( )
A: $\sqrt{2}$
B: $\sqrt{3}$
C: $2 \sqrt{2}$
D: $\sqrt{3}+1$
Answer A.
Analysis Since the two asymptotes are perpendicular to each other, the eccentricity of this hyperbola is the same as that of a hyperbola with asymptotes $y= \pm x$. The equation of a hyperbola with asymptotes $y= \pm x$ is $x^{2}-y^{2}=\lambda(\lambda \neq 0)$, and its eccentricity is $\sqrt{2}$.