Question

$A=\left[\begin{array}{cc}x& -7\\ 7& y\end{array}\right]$ is a skew-symmetric matrix,
then (x,y) =

• A. (1,-1)
• B. (7,-7)
• C. (0,0)
• D. (14,-14)

Answer 1

The correct option is C (0,0)

$A=\left[\begin{array}{cc}x& -7\\ 7& y\end{array}\right]$
Now $A^T=\left[\begin{array}{cc}x& 7\\ -7& y\end{array}\right]$
Now for $A$ to be skew symmetric matrix, $A+A^T=O$
$\Rightarrow \left[\begin{array}{cc}x& -7\\ 7& y\end{array}\right]+\left[\begin{array}{cc}x& 7\\ -7& y\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$
$\Rightarrow \left[\begin{array}{cc}2x& 0\\ 0& 2y\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$
Now equating the corresponding elements we get, $(x,y)=(0,0)$