Matrix Operations Calculator
Perform addition, multiplication, determinant, and inverse operations on 2×2 or 3×3 matrices.
Matrix A
Matrix B
Formulas
Addition: (A+B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ
Multiplication: (A×B)ᵢⱼ = Σₖ Aᵢₖ · Bₖⱼ
2×2 Determinant: det(A) = a·d − b·c
3×3 Determinant (Sarrus/Cofactor):
det(A) = a(ei−fh) − b(di−fg) + c(dh−eg)
2×2 Inverse: A⁻¹ = (1/det(A)) · [[d, −b], [−c, a]]
3×3 Inverse: A⁻¹ = (1/det(A)) · adj(A), where adj(A) is the transpose of the cofactor matrix.
Assumptions & References
- All matrix entries must be real numbers.
- Addition and multiplication require two matrices of the same size.
- Determinant and inverse operate on a single square matrix (Matrix A).
- Inverse exists only when det(A) ≠ 0 (non-singular matrix).
- Results are rounded to 6 significant figures for display.
- Reference: Gilbert Strang, Introduction to Linear Algebra, 5th ed.