Matrix Inverse Calculator

Use our free matrix inverse calculator to find A⁻¹ for any invertible square matrix. Includes verification (A×A⁻¹=I) and step-by-step cofactor/adjugate method.

Math

Mode

Matrix (square)

Formula

The inverse of a square matrix A satisfies A×A⁻¹ = A⁻¹×A = I. Only non-singular matrices (det ≠ 0) are invertible. Uses the cofactor and adjugate method.

A⁻¹ = adj(A) / det(A)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select a mode.
2Enter a square matrix.
3Inverse: computes A⁻¹.
4Verify: checks A×A⁻¹ = I.
5Steps: shows cofactors and adjugate.
6Click Calculate.

Examples

2×2 inverse

1.det = 4×6−7×2 = 10
2.A⁻¹ = (1/10)×[[6,−7],[−2,4]]

Result: 0.6

3×3 inverse

1.det = 1
2.Compute cofactors and adjugate

Result: -24

Frequently Asked Questions

When det(A) ≠ 0 (non-singular).

The transpose of the cofactor matrix.

Cᵢⱼ = (−1)ⁱ⁺ʲ × det(Mᵢⱼ) where Mᵢⱼ is the minor.

For [[a,b],[c,d]]: A⁻¹ = (1/(ad−bc)) × [[d,−b],[−c,a]].

Singular matrices (det = 0) have no inverse.

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CalculateMe Team

Last updated: 2026-07-14

Matrix Inverse Calculator

Formula

How It Works

Examples

2×2 inverse

3×3 inverse

Frequently Asked Questions

When does an inverse exist?

What is the adjugate?

What is the cofactor?

2×2 shortcut?

What about singular matrices?

Related Calculators

Matrix Inverse Calculator

Formula

How It Works

Examples

2×2 inverse

3×3 inverse

Frequently Asked Questions

When does an inverse exist?

What is the adjugate?

What is the cofactor?

2×2 shortcut?

What about singular matrices?

Related Calculators