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Formula verified · Deterministic calculation

Matrix Calculator

Enter two 2×2 matrices and choose addition, subtraction or multiplication. CalcuMint returns the result matrix together with its determinant, trace and visible arithmetic steps.

Matrix A

Matrix B

Result matrix[[19, 22], [43, 50]]
Result determinant
4
Result trace
69
Methodology

Certified 2×2 matrix arithmetic. Addition/subtraction are element-wise; multiplication is row-by-column. Result properties are derived from the same matrix output.

Sources
  • CalcuMint deterministic linear-algebra engine
Solution steps
  1. Operation: A × B
  2. Result = [[19, 22],[43, 50]]
  3. det(result) = 4; trace(result) = 69

How this calculator works

Addition and subtraction operate element by element. Multiplication uses row-by-column products. Determinant and trace are calculated from the resulting 2×2 matrix.

Formula

A+B, A−B, or AB

Performs deterministic addition, subtraction or multiplication on two 2×2 matrices and reports result properties.

Worked example

Multiply matrices is a verified test case used by the calculation engine.

Assumptions and limitations

  • This certified version operates on two 2×2 real matrices.
  • Inputs are finite real numbers.
  • Matrix multiplication follows the standard row-by-column definition.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint. Technical calculation version: 1.

  • CalcuMint deterministic linear-algebra engine — Standard 2×2 matrix arithmetic.

Frequently asked questions

Which operations are supported?

Addition, subtraction and multiplication of two 2×2 matrices.

Does it show result properties?

Yes. It reports the determinant and trace of the result matrix.

Related calculators

Matrix Determinant CalculatorCalculate the determinant of a 2×2 matrix with visible steps.Matrix Inverse CalculatorInvert a non-singular 2×2 matrix with visible steps.RREF CalculatorReduce a 2×3 matrix to reduced row echelon form with visible row operations.