Question

Using the properties of determinants, find the value of

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

Answer 1

Let $\Delta =\left|\begin{array}{ccc}0& a& -b\\ -a& 0& -c\\ b& c& 0\end{array}\right|$
Expanding along first column,
$\Delta =a(0+bc)+b(-ac-0)=abc-abc=0$