There are some properties of Determinants, which are commonly used


Property 1

The value of the determinant remains unchanged if it’s rows and

columns are interchanged

(i.e. |𝐴 𝑇 | = |A|)


Check Example 6


Property 2

If any two rows (or columns) of a determinant are interchanged then sign of determinant changes


Check Example 7


Property 3

If are elements of a row (column) are zero, determinant is 0.



Property 4

If any two rows (or columns) of a determinant are identical, the value of determinant is zero.


Check Example 8 for proof


Property 5

If each element of a row (or a column) of a determinant is multiplied by a constant k, then determinant’s value gets multiplied by k


Check Example 9




Property 6

If elements of a row or column of a determinant are expressed as

sum of two (or more) terms,

then the determinant can be expressed as sum of two (or more) determinants.


Check Example 10 for proof


Property 7

If in a determinant all the elements above or below the diagonal is


then value of the determinant is equal to product of the diagonal elements.


  1. Chapter 4 Class 12 Determinants
  2. Concept wise

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.