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.
After striking a pair of arcs from each endpoint of a line segment, just join the intersection point of the 1st pair (above the segment) with the intersection point of the 2nd pair (under the segment) And this is how you construct the segment's perpendicular bisector