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Matrix Calculator: Determinant, Inverse, Transpose and Multiply

This free matrix calculator finds the determinant, inverse, transpose, trace and rank of a matrix, and adds, subtracts or multiplies two matrices. Type each row on its own line with spaces or commas between values.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

Matrices are the language of graphics, statistics and engineering. Doing the arithmetic by hand is slow and easy to get wrong.

Type your matrix, choose an operation and press the button.

How to Use This Tool

  1. Enter or paste your input in the box or boxes above.
  2. Choose the options, if there are any.
  3. Press the button to run the tool.
  4. Read the result and use the copy button where one is shown.

How the Calculation Works

The determinant and rank use Gaussian elimination with row swaps. The inverse uses Gauss-Jordan elimination on A joined with the identity matrix. Multiplication uses the row-by-column rule. Transpose swaps rows and columns, and the trace adds the diagonal.

Worked Example

The matrix with rows 1 2 and 3 4 has determinant -2. Its inverse has rows -2 1 and 1.5 -0.5.

Common Uses

  • Linear algebra homework.
  • Solving systems of equations.
  • Graphics and transformations.
  • Checking code.

Tips and Common Mistakes

  • Keep sizes up to 10 by 10.
  • A tiny determinant means the matrix is almost singular.
  • Use a full stop for decimals.
  • Check the first result against a case you already know, so you can trust the tool for the rest.
  • Nothing you type leaves your device. The work is done by your browser, so it also works with a slow connection once the page has loaded.

Next, you may need the vector calculator, quadratic equation solver, prime number checker, GCD and LCM calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

Type one row per line. Separate the numbers with spaces or commas. All rows must have the same number of values.
Only for a square matrix whose determinant is not zero.
Each entry is the dot product of a row of A with a column of B, so A must have as many columns as B has rows.
The tool uses ordinary floating point numbers and shows about 10 significant digits.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.