If the matrix $\left[\begin{array}{rrr}0 & -1 & 3 x \\ 1 & y & -5 \\ -6 & 5 & 0\end{array}\right]$ is skew-symmetric, then the value of $5 x-y$ is:

10

The correct answer is Option (3) → 10

$A=\begin{bmatrix}0&-1&3x\\1&y&-5\\-6&5&0\end{bmatrix}.$

$A \text{ skew-symmetric } \Rightarrow A^T=-A.$

$a_{12}=-a_{21} \Rightarrow -1=-1.$

$a_{13}=-a_{31} \Rightarrow 3x=6 \Rightarrow x=2.$

$a_{23}=-a_{32} \Rightarrow -5=-5.$

$a_{22}=-a_{22} \Rightarrow y=0.$

$5x-y=5(2)-0=10.$