#rs/class/math163 #math 
- - -
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
$$\begin{vmatrix}
a&b\\a&b
\end{vmatrix} = ab - ba = 0$$
$$\begin{vmatrix}
r\cdot a&b\\r \cdot c&d
\end{vmatrix} = rad - rbc = r(ad - bc) = r \cdot \begin{vmatrix}
a&b\\c&d
\end{vmatrix}$$

$$\begin{vmatrix}
1&0\\0&1
\end{vmatrix} = 1$$