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

Given $\left[\begin{array}{l}0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}-1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}3\mathrm{x}\\ 1 \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{y}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}-5\\ -6\hspace{0.25em} 5\hspace{0.25em} \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\end{array}\right]$ is skew- symmetric, matrix

$\Rightarrow {\mathrm{a}}_{13}=-{\mathrm{a}}_{31}\Rightarrow 3\mathrm{x}=-(-6)\Rightarrow \mathrm{x}=2$.

Also, ${\mathrm{a}}_{11}={\mathrm{a}}_{22}={\mathrm{a}}_{33}=0\Rightarrow \mathrm{y}=0$

$\therefore$Option (b) is the correct answer.