For a 2 x 2 matrix:
$$ \det\begin{pmatrix}
a&b\\c&d
\end{pmatrix} = \begin{vmatrix} a&b\\c&d\end{vmatrix} = ad-bc$$
For a 3 x 3 matrix:
$$\begin{vmatrix} a&b&c\\d&e&f\\g&h&i\end{vmatrix} = a\begin{vmatrix} e&f\\h&i\end{vmatrix} - b\begin{vmatrix} d&f\\g&i\end{vmatrix} + c\begin{vmatrix} d&e\\g&h\end{vmatrix} = a(ei-hf)-b(di-gf)+c(dh-ge)$$
### Properties
$$\begin{matrix}
a&b\\a&b
\end{matrix}$$