Question

Evaluate the determinants.

$\left|\begin{array}{ccc}0& 1& 2\\ -1& 0& -3\\ -2& 3& 0\end{array}\right|$

Answer 1

Let $A=\left|\begin{array}{ccc}0& 1& 2\\ -1& 0& -3\\ -2& 3& 0\end{array}\right|$
By expanding along $R_1$ (first row), we get
$|A|=0\left|\begin{array}{cc}0& -3\\ 3& 0\end{array}\right|-1\left|\begin{array}{cc}-1& -3\\ -2& 0\end{array}\right|+2\left|\begin{array}{cc}-1& 0\\ -2& 3\end{array}\right|=-1(0-6)+2(-3-0)=-1(-6)+2(-3)=6-6=0$