® 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 ® A square matrix A is said to be singular or non-singular according as
|A| = 0 or |A| ≠ 0 ® If AB = BA = I, where B is square matrix, then B is called inverse of A