If the matrix $A=\left[\begin{array}{ccc}0 & -3 & x+y \\ 3 & x-2 y & 5 \\ -6 & -5 & 0\end{array}\right]$ is skew-symmetric then values of x and y respectively are:

4, 2

The correct answer is Option (4) → 4, 2

$A^T=\left[\begin{array}{ccc}0 & -3 & -6 \\ -3 & x-2 y & -5 \\ x+y & 5 & 0\end{array}\right]$

so $A=-A^T$

$⇒\left[\begin{array}{ccc}0 & -3 & x+y \\ 3 & x-2 y & 5 \\ -6 & -5 & 0\end{array}\right]=\left[\begin{array}{ccc}0 & -3 & 6 \\ 3 & 2 y-x & 5 \\ -x-y & -5 & 0\end{array}\right]$

$x-2y=2y-x$

$⇒x=2y$

$x+y=6$

so $3y=6⇒y=2$

$x=4$