Matrix Calculator
Perform matrix addition, subtraction, multiplication, determinant, inverse, and transpose on 2×2 and 3×3 matrices.
2 × 2
Add (A + B)
Matrix A
Matrix B
Result
0
0
0
0
What is a matrix calculator?
A matrix calculator performs linear-algebra operations on 2×2 and 3×3 matrices — addition, subtraction, multiplication, the determinant, the inverse, and the transpose. These operations underpin systems of equations, computer graphics, and data transformations.
Formulas
(A + B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ | (A − B)ᵢⱼ = Aᵢⱼ − Bᵢⱼ
(AB)ᵢⱼ = Σₖ Aᵢₖ Bₖⱼ | (Aᵀ)ᵢⱼ = Aⱼᵢ
det([[a,b],[c,d]]) = ad − bc
A⁻¹ = adj(A) / det(A)
(AB)ᵢⱼ = Σₖ Aᵢₖ Bₖⱼ | (Aᵀ)ᵢⱼ = Aⱼᵢ
det([[a,b],[c,d]]) = ad − bc
A⁻¹ = adj(A) / det(A)
Example
For A = [[1,2],[3,4]] and B = [[5,6],[7,8]], A + B = [[6,8],[10,12]] and det(A) = 1×4 − 2×3 = −2.
Common Use Cases
- Solving small systems of linear equations.
- Computing transformations in 2D/3D graphics.
- Quickly checking determinant or inverse values by hand.
FAQs
What happens if a matrix is not invertible?
A matrix whose determinant is zero is "singular" and has no inverse. This tool shows a Singular matrix message instead of a numeric result.
Can I multiply matrices of different sizes here?
This tool keeps both matrices the same square size (2×2 or 3×3) so addition, subtraction, and multiplication are always defined.