Properties of Determinants

What are Properties of Determinant?

Properties of the determinant are various properties that are used to easily find the value of determinant of any square matrix.

What is Reflection Property of Determinants?

Reflection properties of determinant is the properties if we interchange any two rows OR any two columns then the value of determinant does not changes only the sign of the determinant changes.

What happens to Determinant if 2 Rows or Columns of the Determinant are interchanged?

The value of the determinant changes its sign when 2 rows or columns are interchanged.

What is All-Zero Property of Determinant?

All-Zero Property of Determinant states that, if in any row or column all the elements are zero then the value of determinant is zero.

What is Sum Property of Determinant?

Sum Property of Determinant stares that, if any row or column all the elements are sum of two numbers then the determinant can be split into two determinant.

What is Triangle Property of Determinant?

Triangle property of determinant states that, if all the elements of below and above the main diagonal are zero. Then the value of the determinant is the product of all the elements of main diagonals.

What we have to study in Properties of Determinant Class 12?

We have to study Triangle Property, sum property, switch property, invariance property, scalar multiple property, transpose property, repetition property and all zero property in Properties of Determinant of Class 12.

Properties of Determinants are the properties that are required to solve various problems in Matrices. There are various properties of the determinant that are based on the elements, rows, and columns of the determinant. These properties help us to easily find the value of the determinant. Suppose we have a matrix M = [a_ij] then the determinant of the matrix is denoted as, |M| or det M.

There are various properties of the determinant of a matrix, and some of the important ones are, Reflection Property, Switching Property, Scalar Multiple Properties, Sum Property, Invariance Property, Factor Property, Triangle Property, Co-Factor Matrix Property, All-Zero Property, and Proportionality or Repetition Property.

In this article, we will learn about all the properties of the determinant with examples and others in detail.