Question

Let A be a skew-symmetric matrix of even order, then $\left|A\right|$

• A. is a square
• B. is not a ssquare
• C. is always zero
• D. none of these

Answer 1

The correct option is A is a square

Let $A=\left[\begin{array}{cc}0& a\\ -a& 0\end{array}\right]$ is a skew-symmetric matrix of order 2.

$|A|=\left|\begin{array}{cc}0& a\\ -a& 0\end{array}\right|=a^2$

$\therefore |A|$ is a perfect square.

Hence option A is correct.