If A is a set, define the identity map on A by idд A → A, idд(a): clearly a bijection. =a. Then idд is Lemma 2: Suppose

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If A is a set, define the identity map on A by idд A → A, idд(a): clearly a bijection. =a. Then idд is Lemma 2: Suppose that f: A→ B and g: B → A satisfy go f = idд, and fog = idg. Then g = f-¹. Hint: You need to prove that g(b): = a f(a) = b. This should not be too much work.