Larger Determinant

Find the determinant of the following 3 x 3 matrix:

Hint
$$$\begin{bmatrix}a & b & c\\ d & e & f\\ g & h & i\end{bmatrix}=a\cdot\begin{vmatrix}e & f\\ h & i\end{vmatrix}-b\cdot \begin{vmatrix}d & f\\ g & i\end{vmatrix}+c\cdot \begin{vmatrix}d & e\\ g & h\end{vmatrix}$$$
Hint 2
$$$\begin{bmatrix}a & b & c\\ d & e & f\\ g & h & i\end{bmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)$$$
For a third-order determinant:
$$$\begin{bmatrix}a & b & c\\ d & e & f\\ g & h & i\end{bmatrix}=a\cdot\begin{vmatrix}e & f\\ h & i\end{vmatrix}-b\cdot \begin{vmatrix}d & f\\ g & i\end{vmatrix}+c\cdot \begin{vmatrix}d & e\\ g & h\end{vmatrix}$$$
$$$\begin{bmatrix}a & b & c\\ d & e & f\\ g & h & i\end{bmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)$$$
Thus,
$$$\begin{bmatrix}1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9\end{bmatrix}=1[(5)(9)-(6)(8)]-2[(4)(9)-(6)(7)]+3[(4)(8)-(5)(7)]$$$
$$$=1[45-48]-2[36-42]+3[32-35]$$$
$$$=1[-3]-2[-6]+3[-3]=-3+12-9=0$$$
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