To solve a determinant of order 4 or higher, one of the lines of the determinant should be formed by zeros, except one: the base element which will be worth 1 or −1.
Follow these steps:
1.If any element of the determinant is 1, choose one of the following lines: the row or column containing the 1. Keep in mind, that the line that contains the largest number of zero elements should be selected.
2.If there is no 1 in the elements:
1.Look at the line containing the maximum number of zero elements and operate so that one of the elements of this line is 1 or −1 (operating with a parallel line).
2.Divide the line by one of its elements, then the determinant should be multiplied by that element so that its value does not vary.
3.Continue to operate until all the elements of the row or column where the basic element is located are zeros.
4.Take the cofactor of the basic element, so that a determinant of order one less than the original is obtained.