Properties of Determinants
Properties of Determinants: Overview
This topic covers concepts such as Properties of Determinants, Equality of Determinant and Its Transpose, Properties of Determinants under Elementary Transformations, Value of a Determinant Having Identical Rows/Columns, etc.
Important Questions on Properties of Determinants
Let and . Such that and . Find the value of .

Using properties of determinants, solve the following for :

The value of the following determinant would be:

The value of given determinant is

If are in A.P then, what would be the value of determinant

If are in A.P then, what would be the value of determinant

Using properties of determinants, the solution for x: would be :


Which of the following operation can prove,

Using properties of determinants, the value of would be

Let then the value of is equal to –

Let , then find the area of given triangle.

Find equation of line joining and using determinants

Find equation of line joining and using determinants

Find equation of line joining and using determinants

Find equation of line joining and using determinants.

Find equation of line joining and using determinants

Let . Then, is equal to

Find equation of line passing through points using determinants.

For all real numbers and , the determinant is equal to
