The determinants associated with square order matrices **no** have the following properties:

P_{1}) When all elements of a row (row or column) are null, the determinant of this matrix is null. Example:

P_{2}) If two rows of an array are equal, then their determinant is null. Example:

P_{3}) If two parallel rows of a matrix are proportional, then their determinant is null. Example:

P_{4}) If the elements of a row in a matrix are linear combinations of the corresponding elements of parallel rows, then their determinant is null. Examples:

P_{5}) **Jacobi's theorem**: The determinant of a matrix does not change when we add to the elements of a row a linear combination of the corresponding elements of parallel rows. Example:

Replacing the 1st column with the sum of that same column twice the 2nd, we have:

Next: Properties (Part 2)