Question

Geometry of elementary row operation does not change determinant

Answer 1

Step-by-step explanation:

two rows (columns) in A are equal then det(A)=0. If we add a row (column) of A multiplied by a scalar k to another row (column) of A, then the determinant will not change. If we swap two rows (columns) in A, the determinant will change its sign. det(A)=det(AT).