If \(A = \begin{bmatrix}0&1&c\\-1&a&-b\\2&3&0\end{bmatrix}\) is a skew-symmetric matrix, then the value of \(a + b + c\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1
In a skew-symmetric matrix \(a_{ji} = -a_{ij}\) for all i, j, so every diagonal element is zero.
Diagonal element \(a_{22}\):
\(a = 0\)
Elements \(a_{13}\) and \(a_{31}\):
\(c = -2\)
Elements \(a_{23}\) and \(a_{32}\):
\(-b = -3\)
\(b = 3\)
Hence
\(a + b + c = 0 + 3 - 2 = 1\)