The number of skew-symmetric matrices of order 3 whose elements are taken from the set \(\{-1, 0, 1\}\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 27
In a skew-symmetric matrix, \(a_{ji} = -a_{ij}\). So every diagonal element is 0, and each element below the diagonal is fixed by the element above it.
\( \displaystyle A = \begin{bmatrix}0&a&b\\-a&0&c\\-b&-c&0\end{bmatrix} \)
Only a, b and c are free. Each can be −1, 0 or 1, and then −a, −b, −c are also in the set.
\(3 \times 3 \times 3 = 27\)