How does the Matrix Inverse Calculator work?

Input square matrix A Then: Calculate inverse using adjugate or Gaussian elimination Then: Verify: A × A⁻¹ = I.

Can you give an example of how to use the Matrix Inverse Calculator?

Example: Input A = [[1,2],[3,4]] gives a result of A⁻¹ = [[-2,1],[1.5,-0.5]].

Is the Matrix Inverse Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Matrix Inverse Calculator?

Our Matrix Inverse Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Matrix Inverse Calculator

Matrix Inverse (2x2)

A[0,0]

A[0,1]

A[1,0]

A[1,1]

Matrix inverse A⁻¹ satisfies A × A⁻¹ = I; used to solve Ax = b as x = A⁻¹ × b.

Symbol	Name	Unit	Description
A	I	—	I
I	I value	—	Variable used in the calculation

Difficulty:intermediate

References

›Matrix Inverse Calc — Wikipedia

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Matrix Inverse Calculator

Matrix Inverse (2x2)

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Matrix Inverse (2x2)