Question

properties of determinants
​

Answer 1

Step-by-step explanation:

There are 10 main properties of determinants which include reflection property, all-zero property, proportionality or repetition property, switching property, scalar multiple property, sum property, invariance property, factor property, triangle property, and co-factor matrix property.

Answer 2

1. If every element of a row (or column )of a square matrix A is zero, then |A| =0

1. If every element of a row (or column )of a square matrix A is zero, then |A| =02. A determinant remains unaltered if the rows are changed into columns or vice versa

1. If every element of a row (or column )of a square matrix A is zero, then |A| =02. A determinant remains unaltered if the rows are changed into columns or vice versa3. If two rows( or columns )of a determinant are interchanged, the sign of the determinant will be changed

4. If two rows( or columns) of a determinant are identical, the value of determinant will be zero

5. If all the elements of one Row(or column) of a determinant is multiplied by a constant 'k' the value of new determinant will be'k' X the value of original determinant

5. If all the elements of one Row(or column) of a determinant is multiplied by a constant 'k' the value of new determinant will be'k' X the value of original determinant6. If to each element of a row (or column) the corresponding elements of another row(or column)multiplied by a constant is added,then the value of determinant remains unaltered