If the matrix \(M = \begin{bmatrix}0 & -1 & 3\alpha\\ 1 & \beta & -5\\ -6 & 5 & 0\end{bmatrix}\) is skew-symmetric, then
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\alpha = 2, \beta = 0\)
In a skew-symmetric matrix, \(M^T = -M\), that is \(m_{ij} = -m_{ji}\) for all i, j. Putting i = j gives \(m_{ii} = -m_{ii}\), so every diagonal entry is 0.
The diagonal entry \(m_{22}\):
\(\beta = 0\)
The entries \(m_{13}\) and \(m_{31}\):
\(3\alpha = -(-6) = 6\)
\(\alpha = 2\)
The other pairs agree: \(m_{12} = -1 = -m_{21}\) and \(m_{23} = -5 = -m_{32}\).