determinants

Here are some rules:

1. Interchanging two rows of A just changes the sign of det(A).
2. Interchanging two columns of A just changes the sign of det(A).
3. If A has a complete row, or column, of zeroes then det(A) = 0.
4. det(A) = det(AT).
5. To any row of A we can add any multiple of any other row without changing det(A).
6. To any column of A we can add any multiple of any other column without changing det(A).

If all the elements of A below (or above) the diagonal are zero then the determinant is equal to the product of the diagonal elements. In particular, the determinant of a diagonal matrix is equal to the product of the diagonal elements.

The determinant of a product is the product of the determinants