Let A be a 3×3 complex matrix and B its transpose. Let a be a complex number such that a≠1 and det(A+a∗B)=0. Compute det(A+B) in terms of a and det(A).
I tried to use the polynomial expansion det(A+xB)=detA+q∗x+w∗x2+detB∗x3 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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