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Let C be the set of all complex numbers. Let S: C 2 ->C 2 is the linear transformation S(x,y) = (ax + by, bx

Let C be the set of all complex numbers. Let S: C2->C2 is the linear transformation S(x,y) = (ax + by, bx + ay) where a,b C and b != 0. Prove S is diagonalizable.

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