The determinant of a nxn matrix can be found using Laplace's method.
Select a column or row (j) to traverse, then calculate the determinant.
The formula is the same, it's just swapping i and j as variables
If you selected a row, then it is:
sum(i=1, n, (-1)^i * a_ij * det(C_ij))
If you chose a column, then:
sum(j=1, n, (-1)^i * a_ij * det(C_ij))
In which:
a_ij means the element on the i-th row and j-th column of the matrix A
C_ij is the cofactor matrix, a matrix equal to A without the i-th row and j-th column