We say that two mappings f and g commute if f ◦ g(z) = g ◦ f(z) for all z. That is, two mappings commute if the order in which you compose them does not change the mapping.
(a) Can a nonidentity translation and a nonidentity rotation commute?
(b) Can a nonidentity translation and a nonidentity magnification commute?
(c) Can a nonidentity rotation and a nonidentity magnification commute?
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