$$[\begin{matrix}3&-2&4\\ 2&0&1\\ 1&2&3\end{matrix}]$$
$20$
$$det(\left(\begin{matrix}3&-2&4\\2&0&1\\1&2&3\end{matrix}\right))$$
$$\left(\begin{matrix}3&-2&4&3&-2\\2&0&1&2&0\\1&2&3&1&2\end{matrix}\right)$$
$$-2+4\times 2\times 2=14$$
$$2\times 3+3\times 2\left(-2\right)=-6$$
$$14-\left(-6\right)$$
$$20$$
$$3det(\left(\begin{matrix}0&1\\2&3\end{matrix}\right))-\left(-2det(\left(\begin{matrix}2&1\\1&3\end{matrix}\right))\right)+4det(\left(\begin{matrix}2&0\\1&2\end{matrix}\right))$$
$$3\left(-2\right)-\left(-2\left(2\times 3-1\right)\right)+4\times 2\times 2$$
$$3\left(-2\right)-\left(-2\times 5\right)+4\times 4$$
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$\left(\begin{matrix}3&-2&4\\2&0&1\\1&2&3\end{matrix}\right)$
