Here are some examples of 2 dimensional transforms and their corresponding 2x2 matrices.
I have noted whether the matrix is symmetric or antisymmetric across the leading diagonal. As you can see, rotation is antisymmetric across the leading diagonal but symmetric along the diagonal, reflection is symmetric across the leading diagonal but antisymmetric along the diagonal. This is not necessarily the case for 3D transforms here.

Identity (symmetric) 


Scale (symmetric) 


Swap x and y axes, which is the same as reflecting in a 45° line (symmetric) 


Swap x and y axes and invert y, which is the same as rotating by 90° (antisymmetric) 


Rotate by angle θ (antisymmetric  but symmetric along the leading diagonal) 


Reflection in x axis  

Reflection in line x,y (see this page) (symmetric  but antisymmetric along the leading diagonal) 
