determinant

For larger matrices, see cofactor expansion.

2x2 matrix determinant

$$\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=ad-cb$$

3x3 matrix determinant

$$\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|=a(ei+hf)-b(di-gf)+c(dh-ge)$$