Question

If A is a skew-symmetric matrix of order $3$ , then find |A|.

Answer 1

A is a skew-symmetric matrix of order $3$

$\Rightarrow A^T=-A$

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

$\Rightarrow det\left(A^T\right)=-det\left(A\right)$

we know $det\left(A^T\right)=det\left(A\right)$

$\Rightarrow det\left(A\right)=-det\left(A\right)$

$\Rightarrow 2det\left(A\right)=0$

$\Rightarrow det\left(A\right)=0$

$\Rightarrow |A|=0$