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|)

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Check Example 6

 

Property 2

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

Properties of determinants - Part 2

Check Example 7

 

Property 3

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

Properties of determinants - Part 3

 

Property 4

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

Properties of determinants - Part 4

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

Properties of determinants - Part 5

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.

Properties of determinants - Part 6

Check Example 10 for proof

 

Property 7

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

zero,

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

Properties of determinants - Part 7

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.