I think you have the right ideas, but your choice of terms is not quite right. What you want to do is to fix a basis (preferably the standard ones) and find the matrices associated with each linear transformation described above. Then you can compose all of these operations by multiplying the associated matrices.

A linear transformation is determined by what it does to the basis. That said, I don't know what you mean by the main diagonal... is it the line ?also, does anyone know how to reflect across the main diagonal in terms such as T(x,y) = (? , ?)o