Show that multiplication by $\displaystyle A = \begin{bmatrix}3 & 1\\ 6 & 2\end{bmatrix}$

maps every point in the plane onto the line $\displaystyle y = 2x$.

I tried to see what happens with the unit square and the points in the unit square is easy to see that they maps onto the line $\displaystyle y = 2x$. But does that equals that every point in the plane maps onto the line?

/regards