® Cofactor of aij of given by Aij = (– 1)i+ j Mij
® Value of determinant of a matrix A is obtained by sum of product of elements
of a row (or a column) with corresponding cofactors For example,
A = a11 A11 + a12 A12 + a13 A13 ® If elements of one row (or column) are multiplied with cofactors of elements
of any other row (or column), then their sum is zero For example, a11 A21 + a12
A22 + a13 A23 = 0
Rationalised 2023-24
 102
MATHEMATICS
® If 
11
12
13
21
22
23
31
32
33
A
,
a
a
a
a
a
a
a
a
a




= 





 then 
11
21
31
12
22
32
13
23
33
A
A
A
A
A
A
A
A
A
A
adj




= 





, where Aij is
cofactor of aij
® A (adj A) = (adj A) A = |A| I, where A is square matrix of order n