Let’s look at what are minors & cofactor of a 2 × 2 & a 3 × 3 determinant
For a 2 × 2 determinant
For
We have elements,
π
11
= 3
π
12
= 2
π
21
= 1
π
22
= 4
Minor will be
π 11 , π 12 , π 21 , π 22
And cofactors will be
π΄ 11 , π΄ 12 , π΄ 21 , π΄ 22
For a 3 × 3 matrix
Minor will be
M 11 , M 12 , M 13 , M 21 , M 22 , M 23 , M 31 , M 32 , M 33
Note : We can also calculate cofactors without calculating minors
If i + j is odd,
A ij = −1 × M ij
If i + j is even,
A ij = M ij
But, why use cofactor?