Verifying properties of a determinant

Chapter 4 Class 12 Determinants (Term 1)
Concept wise

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 all elements of a row (or 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

zero,

then value of the determinant is equal to product of the diagonal elements. Now learn Economics at Teachoo for Class 12 