To evaluate the determinant of order 3 or above, you need to define minors and co-factors.
Let |A| = |[aij]| be a determinant of order n. The minor of an arbitrary element aij is the determinant obtained by deleting the ith row and jth column in which the element aij stands. The minor of aij is denoted by Mij.
The co-factor is a signed minor. The co-factor of aij is denoted by Aij and is defined as
Aij = (−1)i+j Mij