If `A` is a skew-symmetric matrix of odd order `n` , then `|A|=O` .

Explanation

As `A` is skew symmetric matrix of odd order Let $$A=\left[\begin{array}{ccc}0 & 1 & 2 \\ -1 & 0 & 3 \\ -2 & -3 & 0\end{array}\right] \therefore A=-A^{\prime}$$
- (As A is skew symmetric)
$$
\begin{aligned}
&\Rightarrow|A|=|-A||\Rightarrow| A|=-| A \mid \\
&\Rightarrow|A|=-|A| \Rightarrow 2|A|=0 \\
&\therefore|A|=0
\end{aligned}
...