The cofactor helps in the calculation of determinants of order greater than three, because it is used in the Laplace's theorem, since this is used precisely for the calculation of square order matrices n.
Each element of the matrix has its cofactor, and we have the expression that determines the calculation of this cofactor. the cofactor of aij is the number Aij on what:
You must be wondering what is this Dij. We have to Dij is the determinant of the matrix which is obtained through matrix A, however the i-th row and j-th column are eliminated.
This concept will only be understood when we apply it.
Example: Determine the cofactors of the elements: a13 and the22, from matrix A.
As we have seen, to calculate the cofactor of element a13 we're going to use the expression we know from the cofactor.
Note that we need to determine the matrix D13 to calculate its determinant. This matrix will be obtained by eliminating line 1 and column 3 referring to matrix A. Therefore, we have to:
Similarly, we will proceed to find the cofactor of the element a22.
By Laplace's theorem we can relate the cofactors of a matrix to determine the determinant of a matrix with order n.
By Gabriel Alessandro de Oliveira
Graduated in Mathematics
Brazil School Team
Source: Brazil School - https://brasilescola.uol.com.br/matematica/calculando-cofator.htm