Overview

The Matrix Calculator performs addition, subtraction, multiplication, determinant, and inverse calculations for 2×2 and 3×3 matrices. It is useful for linear algebra studies and solving systems of linear equations.

Formula

Matrix addition: (A + B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ

Matrix multiplication: (AB)ᵢⱼ = Σₖ Aᵢₖ × Bₖⱼ

2×2 determinant: det[a b; c d] = ad - bc

2×2 inverse: A⁻¹ = (1/det(A)) × [d -b; -c a]

3×3 determinant: det(A) = a(ei-fh) - b(di-fg) + c(dh-eg) (cofactor expansion)

How to Use

1. 1Select the matrix size (2×2 or 3×3).
2. 2Enter each element of the matrix.
3. 3Select the desired operation (addition, multiplication, determinant, inverse, etc.).
4. 4The resulting matrix or scalar value is displayed.

Tips

• ✔Matrix multiplication is NOT commutative: AB ≠ BA in general.
• ✔If the determinant is 0, the inverse does not exist (singular matrix).
• ✔Multiplying by the identity matrix I returns the original matrix: AI = IA = A.

FAQ