Determinants 3

Now that we know how to find the determinant of a 2 by 2 and 3 by 3 matrix, we know study the formulas. The formula for the determinant of a 2 by 2 matrix, $\left( \begin{array}{ccc}a_{11} & a_{12} \\a_{21} & a_{22} \end{array} \right)$ is $a_{11}a_{22}-a_{12}a_{21}$

And the formula for the determinant of a 3 by 3 matrix, $\left( \begin{array}{ccc}a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\end{array} \right)$

is $a_{11}a_{22}a_{33}+a_{12}a_{23}a_{31}+a_{13}a_{21}a_{32}-a_{12}a_{21}a_{33}-a_{11}a_{23}a_{32}-a_{13}a_{22}a_{32}$

In a n by n matrix, how many terms are there in the formula? (for 2 by 2, it's 2 and for 3 by 3, it's 6)