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: here

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.


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