Question

Explain the properties of determinants in a short way.

Answer 1

1. Property of Reflection:If in a determinant, even when rows are interchanged with columns, the value of the determinant remains unaltered.
2.  All Zero Property:If all the elements of any particular row or any particular column are zero then the value of the determinant is also zero.
3.  Repetition Property:If there are two identical rows or columns then the value of the determinant is zero.
4. Switching Property:If any two rows or columns are interchanged then the value of the determinant changes its sign
5. Property of multiplication by a Scalar:If all the elements of a row or a column in a determinant are multiplied by a constant non-zero value then the value of the determinant also becomes a multiple of that constant
6. Property of Sum:If =∣∣ ∣∣a+xbcd+yefg+zhi∣∣ ∣∣.Then the value of determinant becomes equal to the sum of the determinants obtained by splitting
7. Property of In variance: If any row or column of a determinant is expressed as the sum of multiples of any other row or column then the value of the determinant remains unchanged.
8. Triangle Property:If, in a determinant all the elements above or below the diagonal consists of zero, only then the value of the determinant will be equal to the product of the diagonal element.