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Prove that if the function, phi, G to G' (G and G' are groups) is a homonorphism then the kernel of phi is a normal subgroup of g.

Now let phi be the function from R to GL(2,R) where phi(x) is:
Cos(x) -sin(x)
Sin(x) Cos(x)

Prove that this is a homonorphism, what is the kernel of phi? And what is phi(R)?

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