then the determinant of the identity matrix is one, det(I) = 1.
6. Multiplying a matrix by a number r affects the determinant as follows: det(rA) =
rn det(A).
7. If A contains a zero row (or column), then det(A) = 0.
8. If A contains two identical or proportional rows (or columns), then det(A) = 0.
9. A matrix and its transpose have the same determinant: det(AT ) = det(A).