If the matrix $\left[\begin{array}{ccc}0 & -1 & 3 x \\ 1 & y & -5 \\ -6 & 5 & 0\end{array}\right]$ is skew symmetric, then $6 x+y$ is equal to

12

$A=\left[\begin{array}{ccc}0 & -1 & 3 x \\ 1 & y & -5 \\ -6 & 5 & 0\end{array}\right]~~~~A^{T}=\left[\begin{array}{ccc}0 & 1 & -6 \\ -1 & 4 & 5 \\ 3 x & -5 & 0\end{array}\right]$        (A = -A^T) → skew symmetric

$\Rightarrow\left[\begin{array}{ccc}0 & -1 & 3 x \\ +1 & y & -5 \\ -6 & 5 & 0\end{array}\right]=\left[\begin{array}{ccc}0 & -1 & 6 \\ 1 & -y & -5 \\ -3 x & 5 & 0\end{array}\right]$

So $y = -y ⇒ y = 0$ 

So $3x = 6$

⇒ $x = 2$

$6 x+y$

$=6 \times 2+0=12$