basic

2 × 2 Matrix Multiplication Calculator

Compute the product C = A · B of two 2×2 matrices.

Compute the 2×2 matrix product C = A · B from the eight scalar entries: c₁₁ = a₁₁·b₁₁ + a₁₂·b₂₁; c₁₂ = a₁₁·b₁₂ + a₁₂·b₂₂; c₂₁ = a₂₁·b₁₁ + a₂₂·b₂₁; c₂₂ = a₂₁·b₁₂ + a₂₂·b₂₂.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

C = A · B (entry-wise as above).

In depth

Compute the 2×2 matrix product C = A · B from the eight scalar entries: c₁₁ = a₁₁·b₁₁ + a₁₂·b₂₁; c₁₂ = a₁₁·b₁₂ + a₁₂·b₂₂; c₂₁ = a₂₁·b₁₁ + a₂₂·b₂₁; c₂₂ = a₂₁·b₁₂ + a₂₂·b₂₂.