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,
𝑎
11
= 3
𝑎
12
= 2
𝑎
21
= 1
𝑎
22
= 4
Minor will be
𝑀 11 , 𝑀 12 , 𝑀 21 , 𝑀 22
And cofactors will be
𝐴 11 , 𝐴 12 , 𝐴 21 , 𝐴 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?