Inverse Matrix Calculator

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Introduction

Inverse Matrix Calculator — Find the inverse of a 2x2 matrix. Enter a, b, c, d to get an instant, accurate result.

Formula

For a 2×2 matrix [[a,b],[c,d]] with determinant ad−bc, the inverse is (1/det) × [[d,−b],[−c,a]].

Step-by-step

1. Enter the a.
2. Enter the b.
3. Enter the c.
4. Enter the d.
5. Click Calculate to see your result instantly.

Real-world example

Example: With a = 1, b = 2, c = 3, d = 4, the Inverse Matrix Calculator gives Inverse: -2, 1, 1.5, -0.5, Determinant: -2.

Frequently Asked Questions

When does a matrix have no inverse?

When its determinant is 0 — the matrix is singular and cannot be inverted.

What matrix size is supported?

2×2 matrices.

What inputs does the Inverse Matrix Calculator need?

You'll need to provide: a, b, c, d. All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.

How accurate is the Inverse Matrix Calculator?

The Inverse Matrix Calculator applies the formula exactly as calculated — For a 2×2 matrix [[a,b],[c,d]] with determinant ad−bc, the inverse is (1/det) × [[d,−b],[−c,a]]. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.

Is the Inverse Matrix Calculator free to use?

Yes, the Inverse Matrix Calculator is completely free, requires no signup, and runs instantly in your browser.

About the Inverse Matrix Calculator

The Inverse Matrix Calculator uses a real, verifiable formula — For a 2×2 matrix [[a,b],[c,d]] with determinant ad−bc, the inverse is (1/det) × [[d,−b],[−c,a]]. — so results are accurate every time, not an approximation.