Confirm: 2d transformation matrix cannot change rectangle into isosceles trapezoid?

This non-mathematician needs some help...

Given any 2D transformation matrix as typically used in game programming like this:

$$A=\begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ 0 & 0 & 1 \end{pmatrix}$$

Can anyone confirm that such a matrix cannot be used to convert a rectangle into an isosceles trapezoid?

I don't need a proof, I just need to know it's not possible.

I looked at 2D transformation matrix to make a trapezoid out of a rectangle but I couldn't figure out if the answerers were talking about the typical game 2d matrix or other matrices.