If the matrix \(A = \begin{bmatrix}\alpha & \beta & \gamma\\0 & 0 & 2\\3 & -2 & 0\end{bmatrix}\) is a skew symmetric matrix, then the value of \((\alpha + \beta + \gamma)^2\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 9
In a skew-symmetric matrix, \(a_{ij} = -a_{ji}\) for all i and j. In particular, every diagonal entry is 0.
\(a_{11} = 0:\quad \alpha = 0\)
\(a_{12} = -a_{21}:\quad \beta = -0 = 0\)
\(a_{13} = -a_{31}:\quad \gamma = -3\)
The other entries agree with the condition: \(a_{23} = 2\) and \(a_{32} = -2\).
\((\alpha + \beta + \gamma)^2 = (0 + 0 - 3)^2 = 9\)