The value of the determinant \(\begin{vmatrix}0 & 2 & -3\\ -2 & 0 & 4\\ 3 & -4 & 0\end{vmatrix}\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0
Expanding along the first row:
\( \displaystyle \Delta = 0\begin{vmatrix}0 & 4\\ -4 & 0\end{vmatrix} - 2\begin{vmatrix}-2 & 4\\ 3 & 0\end{vmatrix} + (-3)\begin{vmatrix}-2 & 0\\ 3 & -4\end{vmatrix} \)
\( = 0 - 2(0 - 12) - 3(8 - 0) \)
\( = 24 - 24 \)
\( = 0 \)
This was to be expected: the matrix is skew-symmetric (zero diagonal and \(a_{ji} = -a_{ij}\)), and every skew-symmetric matrix of odd order has determinant 0.