Expand along a row or column using cofactors
Use row operations to simplify the matrix
Convert the matrix to upper triangular form
Multiply the diagonal entries for a triangular matrix
Apply determinant properties:
Swapping two rows changes the sign
Multiplying a row by a scalar multiplies the determinant by that scalar
Adding a multiple of one row to another does not change the determinant
Factor out common terms from rows or columns
Use Sarrus’ rule for 3×3 matrices
Use the formula for 2×2 matrices
Use Laplace expansion for larger matrices
Use block matrix methods when applicable
Use determinant identities and shortcuts when available