Choose a row or column with the most zeros or simplest entries
Expand the determinant by cofactors along that row or column
For each entry (a_{ij}), compute its cofactor (C_{ij} = (-1)^{i+j} M_{ij})
Form each minor (M_{ij}) by deleting row (i) and column (j)
Compute each resulting 3×3 determinant
Multiply each entry by its cofactor
Add the signed products together
Repeat until the 4×4 determinant is fully reduced to 3×3 determinants
Use row operations if helpful, keeping track of how they change the determinant
If the matrix is triangular, multiply the diagonal entries to get the determinant