Question

If $A$ is a skew-symmetric matrix of order $3$, then prove that $detA=0$.

Answer 1

As $A$ is a skew symmetric matrix.
so, $A=-A^T$

$\Rightarrow |A|=|-A^T|$

$\Rightarrow |A|=-|A^T|$ [$\because$ Matrix $A$ is of order $3$].....$\left(i\right)$

Also, we know that

$\Rightarrow |A|=|A^T|\dots \left(ii\right)$

From equation $\left(i\right)$ and $\left(ii\right)$, we get

$|A|=-|A|$

$\Rightarrow 2|A|=0\Rightarrow |A|=0$