For a 2×2 matrix (begin{pmatrix} a & b \ c & d end{pmatrix}), compute (ad – bc)
For a 3×3 matrix, use cofactor expansion or Sarrus’ rule
For an (n times n) matrix, expand along any row or column using cofactors
Choose an entry (a_{ij})
Compute its minor by deleting row (i) and column (j)
Multiply the minor by ((-1)^{i+j}) to get the cofactor
Sum all entries in the chosen row or column times their cofactors
Use row operations to simplify the matrix before expanding
Swap two rows and change the sign of the determinant
Multiply a row by a scalar and multiply the determinant by the same scalar
Add a multiple of one row to another row without changing the determinant
For triangular matrices, multiply all diagonal entries
For block diagonal matrices, multiply the determinants of the blocks
For singular matrices with dependent rows or columns, the determinant is 0