## Group theory - orbits and fixed points (please help!)

I have my Group Theory exam in less than a month and I can't get to grips with orbits and stabilizers. Please could someone talk me through the solution to this question?

Let $G=GL(2,\mathbb R)$ and $X=\mathbb R^{2}$.

Let $G\times X\rightarrow X,$ $
\left(\begin{array}{ccc}
\left(\begin{array}{cc}
a & b\\
c & d\end{array}\right) & , & \left(\begin{array}{c}
x\\
y\end{array}\right)\end{array}\right)\mapsto\left( \begin{array}{ccc}
ax & + & by\\
cx & + & dy\end{array}\right),
$
define a G action.

What are the orbits and fixed point sets of this G action?