Consider the linear transformation from
to
given by x
Ax
where

We can examine this by looking at inputs and outputs, the images of those inputs under the linear transformation. In the following movie the inputs are in red and the outputs are in blue. Each of the inputs is a unit vector. The initial input is the vector (1 0)T. It doesn't show because it is hiding on the horizontal axis.
To restart the animation, just double click on it.
To stop the animation at any point, just click on it.
To restart it, double click again.