If A is a skew-symmetric matrix of order 3 × 3,

Given: A is a skew-symmetric matrix of order 3 × 3

$A=-A^{T}$

Taking determinant on both sides, we get

$\Rightarrow|A|=\left|-A^{T}\right|$

$\Rightarrow|A|=(-1)^{3}\left|A^{T}\right| \quad(\because$ Order of $A$ is $3 \times 3)$

$\Rightarrow|A|=(-1)^{3}|A| \quad\left(\because\left|A^{T}\right|=|A|\right)$

$\Rightarrow|A|=-|A|$

$\Rightarrow|A|+|A|=0$

$\Rightarrow 2|A|=0$

$\Rightarrow|A|=0$

Hence, $|A|=\underline{0}$.