# Matrix Transformation for 2D, how do I tell what this matrix does geometrically?

Given a 2x2 matrix, $$\begin{bmatrix}1&-1\\-1&\frac12\end{bmatrix}$$ What geometric effect does it have?

So a way I did to solve this was to simply apply it to a unit square that I drew on a graph paper and see what the new image looks like.

Picture of transformation:

To me it looks like a reflection, followed by shearing. But this is where I get lost...

I understand that you can first do a rotation, followed by a shear, and the product of these two transformation matrix will give you a matrix that does the two transformation.

I guess what I'm specifically asking is, is there a way to derive how I can get to this $$A$$ matrix?

Or am I wrong to think of it that way.