Question

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

Answer 1

L.H.S

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

On expanding w.r.t $R_1$, we get

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

$\Rightarrow 0-abc+abc-0$

$\Rightarrow 0$

R.H.S

Hence, proved.