Question

with a general form of a 3×3 skew matrix and prove that it's determinent is zero

Answer 1

$\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\-a_{12}&a_{22}&a_{23}\\-a_{13}&-a_{23}&a_{13}\end{array}\right]$

$\left|\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\-a_{12}&a_{22}&a_{23}\\-a_{13}&-a_{23}&a_{13}\end{array}\right|$