The determinant of a square matrix M = a_{ij}_{mxn} can be obtained by summing the products of the elements of any row (row or column) of the matrix **M** by their cofactors.

So setting we have:

on what is the sum of all index terms **i**ranging from 1 to **m**, .

Example:

Calculate the determinant of matrix A by applying the Laplace Theorem:

Highlighting the second line of the matrix, we have D = 5. THE_{21} + 0. THE_{22} + 1. THE_{23} + (-3). THE_{24}. Let's calculate the cofactors:

Finally, we calculate the determinant:

D = 5. THE_{21} + 0. THE_{22} + 1. THE_{23} + 3. THE_{24}

D = 5. (-411) + 0. (462) + 1. (60) + (-3). (-399)

D = -2055 + 0 + 60 + 1197**D = - 798**