Evaluate the determinants
$\left|\begin{array}{ccc}0 & 1 & 2 \\ -1 & 0 & -3 \\ -2 & 3 & 0\end{array}\right|$
Evaluate the determinants
$\left|\begin{array}{ccc}0 & 1 & 2 \\ -1 & 0 & -3 \\ -2 & 3 & 0\end{array}\right|$
Let $A=\left[\begin{array}{ccc}0 & 1 & 2 \\ -1 & 0 & -3 \\ -2 & 3 & 0\end{array}\right]$
By expanding along the first row, we have:
$|A|=0\left|\begin{array}{ll}0 & -3 \\ 3 & 0\end{array}\right|-1\left|\begin{array}{ll}-1 & -3 \\ -2 & 0\end{array}\right|+2\left|\begin{array}{ll}-1 & 0 \\ -2 & 3\end{array}\right|$
$=0-1(0-6)+2(-3-0)$
$=-1(-6)+2(-3)$
$=6-6=0$
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