Question

If $A$ is a skew symmetric matrix of even order then $det\left(A\right)$ is

• A. $0$
• B. $\ne 0$
• C. non zero perfect square
• D. None of these

Answer 1

The correct option is C non zero perfect square

Since $A$ is skew-symmetric hence

$A^T=-A$

$\Rightarrow \left|A^T\right|=|-A|={(-1)}^{2m}\left|A\right|=\left|A\right|$

$\Rightarrow \left|A\right|=\left|A\right|$

Then $det\left(A\right)$ is non zero perfect square