6. Show the ring {a+bv2|z, b € Z} has exactly 2 automorphisms. These are the identity and the map which switches sign on the square root. Show they preserve addition and multiplication. Any automorphism must be linear and must be the identity on the integers. The only question is what happens to the square root. It must go to an element whose square is 2.

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A: Given

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A: Please see the next step for details

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Q: ould we also use Cantor's diagonalization to contradict this as well?

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A: I have write answers below Explanation: