Basic rules for computing determinants (of any order):
• A determinant of order n can be reduced to n determinants
of order n − 1 by ”expanding/developing” it along any of its
rows/columns, according to the rule of alternative signs.
• Adding to a row/column of a determinant a scalar multiple of
another row/column, does not change the numerical value of
the determinant.
• A determinant with two proportional rows (or two proportional
columns) is equal to zero.
• Switching two rows/columns, changes the sign of the determinant.
• A common factor of all numbers in a row/column can be taken
in front of the determinant.
• Transposing a determinant (that is, making all rows of the determinant into columns of corresponding rank) does not change
the value of the determinant.
1