Math basics › Linear algebra
Determinants and inverses
2 × 2
det [[a, b], [c, d]] = ad − bc.
What it tells you
det A = 0 means A has no inverse: its columns are dependent, and Ax = b has no unique solution.
A 2 × 2 inverse
Swap a and d, change the signs of b and c, and divide everything by ad − bc.
Bigger ones
Expand along the row or column with the most zeros, or row reduce: a swap flips the sign, scaling a row scales the determinant, and adding a multiple of a row changes nothing.