Question

thought provoking is the composition of a rotation and a dilation commutative? (in other words, do you obtain the same image regardless of the order in which you perform the transformations?)
no; only a composition of transformations of the same type is commutative.
no; the composition of a rotation and a dilation is never commutative because rotations are rigid motions while dilations are similarity transformations.
sometimes; as long as the center of dilation and the center of rotation are the same, the composition of a rotation and a dilation is commutative.
yes; rotations do not change the size of a figure, while dilations only change the size of a figure. so, the composition of a rotation and a dilation is commutative.

Explanation:

When the center of rotation and center of dilation are the same point, rotating a figure then dilating it (using that shared center) produces the same result as dilating first then rotating. If the centers are different, the order of transformations will result in different final positions/sizes of the figure, so the composition is only commutative under the condition of shared centers.

Answer:

sometimes; As long as the center of dilation and the center of rotation are the same, the composition of a rotation and a dilation is commutative.