# This problem is about abstract algebra, especially is group theory. Let G=GL2(C). which means gen... this problem is about abstract algebra, especially is group theory.

Let G=GL2(C). which means general linear group with each components are complex number.

and let H = {2x2 matrix (a b ; c d) l a,b,c are in Complex number, ac is not zero}

Prove that every element of G is conjugate to some element of the subgroup H and deduce that G is the union of conjugates of H [ Show that every element of GL2(C) has an eigenvector ]

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