# Isomorphism

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If G ={a + b*sqrt2 | a,b rational} and H = {matrix a 2b, b a | a,b rational}, H is a 2 x 2 matrix -

a 2b

b a

show that G and H are isomorphic under addition. Prove that G and H are closed under multiplication.

I know I need to define the function map first, but I don't know what it is in this problem, let alone prove that it is one-to-one and onto. Any help would be much appreciated.

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#### Solution Summary

This shows how to show that sets are isomorphic under addition and closed under multiplication.

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