Let A be a 3×3 complex matrix and B its transpose. Let a be a complex number such that a≠1 and det. Compute \det(A+B) in terms of a and \det(A).
I tried to use the polynomial expansion \det(A+xB)=\det A + q*x +w*x^2+ \det B*x^3 for any matrices A,B. Probably I should have found some relations between coefficients q and w beacuse B is A transposed, but got stuck.
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