What does a zero determinant mean?

A determinant of zero means the matrix is singular — it has no inverse, and any system of equations it represents has either no solution or infinitely many solutions.

What method is used to compute the determinant?

For 2x2 matrices, the standard ad-bc formula is used. For 3x3 and 4x4, cofactor expansion (Laplace expansion) along the first row is applied, breaking the problem into smaller sub-determinants.

Can I enter negative or decimal values?

Yes. Any real number is accepted, including negative numbers and decimals like -3.14 or 0.5. Results are rounded to 6 significant figures to avoid floating-point noise.

Why does the step-by-step show 2x2 sub-determinants?

Cofactor expansion reduces an n×n determinant to a sum of (n-1)×(n-1) determinants. For a 4x4 matrix, the tool expands twice — first to 3x3, then each 3x3 to 2x2 — matching standard textbook notation.

Is there a size limit?

The tool supports 2x2, 3x3, and 4x4 matrices. These cover the vast majority of coursework and practical use cases. Larger matrices are typically handled by software like MATLAB or NumPy.

Matrix Determinant Calculator

Enter matrix values, pick a size (2x2, 3x3, or 4x4), and instantly see the determinant with full step-by-step working.

Matrix Input

Enter matrix values and click Calculate

Summary

This tool computes the determinant of square matrices up to 4x4. Enter your matrix values, choose the size, and click Calculate to get the result. Full step-by-step working is displayed — including cofactor expansions and 2x2 sub-determinants — so you can verify every intermediate step.

How it works

Select the matrix size: 2x2, 3x3, or 4x4.
Fill in the matrix cells with numeric values (decimals allowed).
Click "Calculate Determinant" to run the computation.
The determinant value is shown with color-coded step-by-step working.
Use "Clear" to reset the grid, or "Random" to load a sample matrix.

Use cases

Check whether a matrix is invertible (determinant ≠ 0).
Verify homework or exam answers with shown working.
Solve systems of linear equations using Cramer's Rule.
Understand cofactor expansion step by step.
Quick sanity-check during linear algebra coursework.
Prepare examples for teaching or tutoring sessions.

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu