Question

If $P=\left[\begin{array}{ccc}0& 4& -2\\ x& 0& -y\\ 2& -8& 0\end{array}\right]$ is a skew-symmetric matrix, then x-y =

• A. 8
• B. 4
• C. -12
• D. -8

Answer 1

The correct option is B 4

P is skew-symmetric matrix.

Therefore,

$P^T=-P$

$\left[\begin{array}{ccc}0& x& 2\\ 4& 0& -8\\ -2& -y& 0\end{array}\right]=\left[\begin{array}{ccc}0& -4& 2\\ -x& 0& y\\ -2& 8& 0\end{array}\right]$

Therefore,

$x=-4$ and $y=-8$

$⟹x-y=-4+8=4$.