(5) Recall that an element of a ring is idempotent if a² = a. (a) Show that any integral domain can have only 1 and 0 as idempotent elements. (b) Is the converse to the previous statement true? Hint: Consider the ring of continuous functions defined on the interval [0, 1], which we call C([0, 1]). What are the idempotent elements? Is this ring an integral domain?

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