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Formula verified · Deterministic calculation

Matrix Inverse Calculator

Calculate the inverse of a 2×2 matrix and inspect its determinant and deterministic transformation steps.

Inverse matrix[[0.6, -0.7], [-0.2, 0.4]]
Determinant
10
Row 1 · Col 1
0.6
Row 1 · Col 2
-0.7
Row 2 · Col 1
-0.2
Row 2 · Col 2
0.4
Methodology

The certified engine applies the 2×2 inverse identity only when the determinant is non-zero.

Sources
  • CalcuMint deterministic linear-algebra engine
Solution steps
  1. det = ad - bc = 10
  2. A⁻¹ = (1/10)[[6, -7],[-2, 4]]
  3. A⁻¹ = [[0.6, -0.7],[-0.2, 0.4]]

How this calculator works

For A=[[a,b],[c,d]], A⁻¹=(1/(ad-bc))[[d,-b],[-c,a]] when ad-bc is non-zero.

Formula

A⁻¹=(1/(ad-bc))[[d,-b],[-c,a]]

Computes the inverse of a non-singular 2×2 matrix.

Worked example

Inverse of [[4,7],[2,6]] is a verified test case used by the calculation engine.

Assumptions and limitations

  • This certified version supports 2×2 matrices.
  • The matrix determinant must be non-zero.

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 inverse identity.

Frequently asked questions

Can every 2×2 matrix be inverted?

No. A matrix with determinant zero is singular and has no inverse.

Is the determinant shown?

Yes. The determinant used by the inverse calculation is displayed.

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Matrix Determinant CalculatorCalculate the determinant of a 2×2 matrix with visible steps.System of Equations SolverSolve a two-variable linear system with deterministic steps.
Matrix Inverse Calculator | CalcuMint