Perform matrix operations: addition, subtraction, multiplication, transpose, determinant, inverse, and scalar multiplication for 2×2 and 3×3 matrices.
Enter matrix values to see results.
| Operation | Formula / Notes |
|---|---|
| Addition | C[i,j] = A[i,j] + B[i,j] |
| Multiply | C[i,j] = Σ A[i,k]·B[k,j] |
| Transpose | Aᵀ[i,j] = A[j,i] |
| det(2×2) | ad − bc |
| det(3×3) | Cofactor expansion along row 1 |
| Inverse 2×2 | (1/det)·[[d,−b],[−c,a]] |
| Inverse 3×3 | (1/det)·adjugate(A) |
| Scalar | (kA)[i,j] = k·A[i,j] |
| Property | Formula |
|---|---|
| (AB)ᵀ | = BᵀAᵀ |
| (AB)⁻¹ | = B⁻¹A⁻¹ |
| det(AB) | = det(A)·det(B) |
| det(Aᵀ) | = det(A) |
| A·A⁻¹ | = I (identity matrix) |