If a, b, c are complex numbers, then the determinant $Δ=\begin{vmatrix}0&-b&-c\\\bar b&0&-a\\\bar c&\bar a&0\end{vmatrix}$, is
Answer & explanation
Correct answer: option 2
We observe that
$\overline{Δ}=\begin{vmatrix}0&-\overline b&-\overline c\\b&0&-\overline a\\c&a&0\end{vmatrix}$
$⇒\overline{Δ}=-\begin{vmatrix}0&\overline b&\overline c\\-b&0&\overline a\\-c&-a&0\end{vmatrix}$ [Taking (-1) common from each row]
$⇒\overline{Δ}=-\begin{vmatrix}0&-b&-c\\\overline b&0&-a\\\overline c&\overline a&0\end{vmatrix}$ [Interchanging rows and columns]
$⇒\overline{Δ}=-Δ⇒Δ+\overline{Δ}=0$ ⇒ Δ is purely imaginary.