If the matrix $A=\begin{bmatrix}α&β&γ\\0&0&2\\3&-2&0\end{bmatrix}$ is a skew symmetric matrix, then the value of $(α+β+γ)^2$ is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 9
A matrix A is skew-symmetric if Aᵀ = -A, which implies:
1. Diagonal elements must be 0 → α = 0, a₂₂ = 0 ✔, a₃₃ = 0 ✔
2. Off-diagonal elements satisfy aᵢⱼ = -aⱼᵢ
Given matrix:
A = $\begin{bmatrix} \alpha & \beta & \gamma \\ 0 & 0 & 2 \\ 3 & -2 & 0 \end{bmatrix}$
$a₁₃ = γ → a₃₁ = 3 → γ = -3$
$a₁₂ = β → a₂₁ = 0 → β = 0$
Diagonal: α = 0
Therefore, α + β + γ = 0 + 0 + (-3) = -3
$(\alpha + \beta + \gamma)^2 = (-3)^2 = 9$