If you apply two translations, then order doesn't matter. However, if you apply a translation and a rotation, then the order will matter because you'll be able to get two different image outputs. So it depends on what the transformations are.
A combination of two rigid transformations on a pre image will Sometimes produce the same image when taken in a different order.
A rigid transformation is a transformation of the plane, which preserves length. There are many types of transformations - reflections, translations, rotations, and also their combinations.
