▦ Matrix Calculator

About the Matrix Calculator

This calculator runs entirely in your browser. It performs the most common 2×2 matrix operations: addition, subtraction, matrix multiplication, determinant, and transpose. Enter the elements of matrices A and B, pick an operation, and the result appears instantly.

Matrix formulas

• Addition — A + B adds corresponding elements: (aᵢⱼ + bᵢⱼ).
• Subtraction — A − B subtracts corresponding elements: (aᵢⱼ − bᵢⱼ).
• Multiplication — C = A × B where cᵢⱼ = Σ aᵢₖ · bₖⱼ. For 2×2: c₁₁=a₁₁b₁₁+a₁₂b₂₁, c₁₂=a₁₁b₁₂+a₁₂b₂₂, etc. Note: order matters (A×B ≠ B×A in general).
• Determinant — det(A) = a₁₁·a₂₂ − a₁₂·a₂₁. A scalar; zero when A is singular (non-invertible).
• Transpose — Aᵀ swaps rows and columns: (Aᵀ)ᵢⱼ = aⱼᵢ.

How to use the calculator

1. Enter the four elements of matrices A and B.
2. Click the button for the operation you need.
3. The result matrix (or scalar) appears below. Each button can be pressed repeatedly.

Frequently asked questions

Why only 2×2 matrices? This keeps the tool simple and fast for the most common linear-algebra cases. Larger matrices require a more complex input UI.

Does matrix multiplication order matter? Yes. In general A × B ≠ B × A. The "A × B" button computes A multiplied by B (A on the left).

What does a zero determinant mean? A determinant of zero means the matrix is singular — it has no inverse and its rows (or columns) are linearly dependent.

Is my input stored or uploaded? No. Everything happens in your browser. Your input is never sent to a server.