If we have a 2 x 2 matrix

$\displaystyle \displaystyle \begin{bmatrix}a&b\\

c&d\end{bmatrix}$

the determinant is given by $\displaystyle \displaystyle ad - bc$

If we have a 3 x 3 matrix

$\displaystyle \displaystyle \begin{bmatrix}a&b&c\\

d&e&f\\g&h&i\end{bmatrix}$

the determinant is given by $\displaystyle aei + bfg + cdh - afh - bdi - ceg$

Is there such a formula for a 4 x 4 matrix

$\displaystyle \displaystyle \begin{bmatrix}a&b&c&d\\

e&f&g&h\\i&j&k&l\\m&n&o&p\end{bmatrix}$