Example 8 Find the minor of element 6 in the determinant 
1
2
3
4
5
6
7
8
9
∆ =
Solution Since 6 lies in the second row and third column, its minor M23 is given by
M23 =
1
2
7
8  = 8 – 14 = – 6 (obtained by deleting R2 and C3 in ∆) Definition 2 Cofactor of an element aij, denoted by Aij is defined by
Aij = (–1)i + j Mij, where Mij is minor of aij Example 9 Find minors and cofactors of all the elements of the determinant 
1
–2
4
3
Solution Minor of the element aij is Mij
Here a11 = 1 So M11 = Minor of a11= 3
M12
 = Minor of the element a12 = 4
M21 = Minor of the element a21 = –2
M22 = Minor of the element a22 = 1
Now, cofactor of aij is Aij