If the matrix $M =\begin{bmatrix}0&-1&3α\\1&β&-5\\-6&5&0\end{bmatrix}$ is skew- symmetric, then

$α=2,β=0$

The correct answer is Option (3) → $α=2,β=0$

Given matrix: $M = \begin{bmatrix} 0 & -1 & 3\alpha \\ 1 & \beta & -5 \\ -6 & 5 & 0 \end{bmatrix}$

Property of skew-symmetric matrix: $M^T = -M$, so diagonal elements = 0 and $a_{ij} = -a_{ji}$

Check elements:

(1,3) element: 3α, (3,1) element: -6 → 3α = 6 ⇒ α = 2

(1,1), (2,2), (3,3) diagonal elements: 0, β, 0 ⇒ β = 0

Values: α = 2, β = 0