Question: Suppose that * is an associative binary operation on a set S. Let H = {a S| a * x = x * a

Suppose that * is an associative binary operation on a set S. Let H = {a ∈ S| a * x = x * a for all x ∈ S}. Show that H is closed under *· (We think of H as consisting of all elements of S that commute with every element in S.)

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