Question

$\left|\begin{array}{c}0\\ -a\\ b\end{array}\begin{array}{c}a\\ 0\\ c\end{array}\begin{array}{c}-b\\ -c\\ 0\end{array}\right|=0$

Answer 1

$\left|\begin{array}{ccc}1& a& -b\\ -a& 0& -c\\ b& c& 0\end{array}\right|$

$=0(0+c^2)-a(0+bc)-b(-ac-0)$

$=-abc+abc$

$=0$