liminfo

Matrix Calculator

Free web tool: Matrix Calculator

Matrix A

Matrix B

About Matrix Calculator

The Matrix Calculator is a free browser-based tool for performing common linear algebra operations on square matrices. It supports matrix sizes from 2x2 up to 4x4, and covers six operations: addition (A+B), subtraction (A-B), multiplication (A×B), transpose, determinant, and matrix inverse — covering the core calculations needed in courses, engineering projects, and data science workflows.

This tool is primarily used by students learning linear algebra, engineers solving systems of linear equations, and data scientists working with transformation matrices. You can enter any real-number values into the cell inputs, select the desired operation, and get the result instantly without any formulas to remember or software to install.

Technically, all matrix arithmetic is implemented in-browser using pure JavaScript. Determinant calculation uses cofactor expansion (Laplace expansion), while matrix inversion uses the adjugate method: computing the cofactor matrix, transposing it to get the adjugate, then dividing by the determinant. Results are displayed with up to 4 decimal places of precision, stripping trailing zeros for clean output.

Key Features

  • Supports 2x2, 3x3, and 4x4 square matrix sizes selectable from a dropdown
  • Six operations: addition, subtraction, multiplication, transpose, determinant, and inverse
  • Individual cell inputs for precise entry of integer or decimal values
  • Determinant computed via cofactor (Laplace) expansion, accurate for any size
  • Inverse calculated using the adjugate method with determinant check
  • Clear error message when the inverse does not exist (determinant = 0)
  • 100% client-side processing — all calculations happen in the browser
  • Dark mode support and responsive grid layout for desktop and mobile

Frequently Asked Questions

What operations does the Matrix Calculator support?

It supports six operations: addition (A+B), subtraction (A-B), multiplication (A×B), transpose of A, determinant of A, and inverse of A. All results are displayed in an output matrix grid, except the determinant which is a scalar value.

What matrix sizes can I calculate?

You can choose 2x2, 3x3, or 4x4 square matrices from the size selector. All six operations work for every size. Changing the size resets both matrices to zero.

How is the determinant calculated?

The determinant is computed using cofactor (Laplace) expansion along the first row, applied recursively. For a 2x2 matrix, it uses the direct formula ad-bc. For 3x3 and 4x4, it expands by minors.

How is the matrix inverse calculated?

The inverse is computed using the adjugate method: the cofactor matrix is transposed to get the adjugate, then each element is divided by the determinant. If the determinant is zero, the matrix is singular and has no inverse — the tool displays an error in that case.

What happens if I try to invert a singular matrix?

If the determinant of your matrix is zero, the matrix is singular and an inverse does not exist. The tool will show an error message explaining this, rather than displaying an incorrect result.

Can I enter decimal or negative numbers?

Yes. Each cell accepts any real number, including negative values and decimals. The result is displayed with up to 4 significant decimal places, with trailing zeros removed for readability.

Is the Matrix Calculator free?

Yes, it is completely free with no usage limits, no advertisements that block functionality, and no account required. It is part of liminfo.com's collection of free online math tools.

Is my data safe when using this tool?

Absolutely. All calculations happen entirely within your web browser. No matrix data is ever sent to a server, stored in a database, or shared with third parties.