Basic Properties of Determinants

Important Properties of Determinants

There are 10 important properties of determinants that are widely used. The description of each of the 10 important properties of determinants are given below.

1. Reflection Property

The reflection property of determinants defines that determinants do no change if rows are transformed into columns and columns are transformed into rows.

2. All- Zero Property

The determinants will be equivalent to zero if each term of rows and columns are zero.

3. Proportionality (Repetition Property)

If each term of rows or columns is similar to the column of some other row (or column) then the determinant is equivalent to zero.

4. Switching Property

The interchanging of any two rows (or columns) of the determinant changes its signs.

5. Factor Property

If a determinant Δ beomes 0 while considering the value of x  = α, then (x -α) is considered as a factor of Δ.