I want to create a transformation matrix $T$ based off of a few things...
First, I rotate clockwise by some angle $\theta$ with matrix $A$, then I scale by some factor $k$ with matrix $B$, then I reflect about some line $l$ with some matrix $C$.
Why does $T = CBA$ and not $T = ABC$? I would think that the multiplication would follow the order, but apparently it doesn't. Why is this true?