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Deal with combining rigid motions. Given two rigid motions M and N, we can combine the two rigid motions by first applying it and then applying X to the result. The rigid motion defined by combining M and N (M goes first, N goes second) is called the product of M and N. In each case, state whether the rigid motion M is proper or improper. (a) M is the product of a proper rigid motion and an improper rigid motion. (b) M is the product of an improper rigid motion and an improper rigid motion. (c) M is the product of a reflection and a rotation. (d) M is the product of two reflections.