Determinants - Definition

Every square matrix can be associated to an expression or a number which is known as determinant.

If the matrix has only one element a11 then a11 is the determinant.

If the matrix is of order 2 that 2 by 2 matrix

|A| =

|a11 a12|
|a21 a22| =

a11*a22 – a12*a21

Determinant of a square matrix of order 3

Determinant of a square matrix of order 3 is the sum of the product of elements a1j in the first row with (-1) 1+j times the determinant of a 2×2 sub-matrix obtained by leaving the first row and column passing through the element.



(i) Only square matrices have determinants.
(ii) The determinant of a square matrix of order three can be expanded along any row or column.

Determinant of a square matrix of order 4 or more

(iii) Determinant of a square matrix of order 4 or more can be determined following the procedure of finding the determinant of a square matrix of order 3. But in this case, especially in the case of 4×4 matrix, when we omit the rows and columns containing the elements of a row, we get 3×3 sub-matrices and we have to find determinants for them.