Adjust the inputs below. Results update as you type.
Matrix multiplication: (AB)ᵢⱼ = Σ Aᵢₖ Bₖⱼ—not commutative (AB ≠ BA generally). Determinant of 2×2: ad − bc. Inverse exists only when det ≠ 0. Gauss-Jordan elimination finds the inverse by row-reducing [A|I] to [I|A⁻¹]. Matrices model linear transformations, solve systems of equations, and represent adjacency in graph theory.
2×2 matrices A · B
det(A) = -2
A·B = [[19.00, 22.00], [43.00, 50.00]]