Three lines are given by the equations:
$$\begin{aligned} & a x + b y + c = 0 \\ & b x + c y + a = 0 \\ & c x + a y + b = 0 \end{aligned}$$
where $a$, $b$ and $c$ are non-zero real numbers. Which one of the following is correct? A If two of the lines are parallel, then all three are parallel. B If two of the lines are parallel, then the third is perpendicular to the other two. C If two of the lines are parallel, then the third is parallel to $y = x$. D If two of the lines are parallel, then the third is perpendicular to $y = x$. E If two of the lines are perpendicular, then all three meet at a point. F If two of the lines are perpendicular, then the third is parallel to $y = x$. G If two of the lines are perpendicular, then the third is perpendicular to $y = x$.