Determinant of a Matrix

Scalar that tells whether a matrix is invertible.

det [a c b d] = a d - b c

Variables

Geometrically, $∣ det A ∣$ is the area (or volume) scale factor of the transformation. Larger matrices use cofactor expansion or row reduction.

$det [1324] = 4 - 6 = - 2$ .

Matrix determinant, inverse, transpose, RREF, rank, eigenvalues, multiplication and addition with steps.

Inverse of a 2×2 Matrix

Swap the diagonal, negate the off-diagonal, divide by the determinant.

Cramer's Rule

Solves square linear systems with determinants.