If and are angles of a triangle

MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants

Problem

A, B

and

C

are angles of a triangle, the value of

\begin{vmatrix} e^{2iA} & e^{-iC} & e^{-iB} \\ e^{-iC} & e^{2iB} & e^{-iA} \\ e^{-iB} & e^{-iA} & e^{2iC} \end{vmatrix}

is (where

i = \sqrt{-1}

) (1) 1 (2) -1 (3) -2 (4) -4