Consider glide reflections as well as compositions of translations and reflections that are not glide reflections.
Not commutative.
Practice makes perfect
If the reflection is perpendicular to the direction of this translation, the order in which you perform the translations does not matter. In other words, a glide reflection is commutative. Consider the following glide reflection
Translation:& (x,y)→ (x+5,y+5)
Reflection:& in the line y=x.
Regardless of the order we perform these transformations, the red triangle will be our image.
However, any time the translation isn't parallel to the line of reflection, the order in which you perform the transformations does matter. Consider the following combinations of transformations:
Translation:& (x,y)→ (x+8,y+1)
Reflection:& in the x-axis
Start with the green triangle. Performing the translation first, we end up with the red triangle as our image. However, reversing the order of transformations, the purple triangle will be our image.
