The set C1(R) ⊂C(R) is the set of differentiable real-valued functions with domain R. Consider C1(R) as a ring and show that it is not an integral domain

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Q: 2. Prove that if A is nonsingular, then Aª is nonsingular and (AT)−¹ = (A−¹)T. Hint: (AB)T = BT AT.

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Q: Show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

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