If \begin{vmatrix}2&3+i&-1\\ 3-i&0&i-1\\ -1&-1-i&1\end{vmatrix}=A+iB where i=\sqrt{-1}, then what is A+B equal to?

Explanation

The given matrix is Hermitian because a_{ij} = \overline{a_{ji}}. The determinant of a Hermitian matrix is always a purely real number, so B = 0. Evaluating the determinant yields -6, so A = -6. Thus A+B = -6.

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