Matrix multiplication
To multiply A × B, each entry of the result is the dot product of a row of A with a column of B. The number of columns in A must equal the number of rows in B, and the result has A's rows and B's columns. Matrix multiplication isn't commutative: A × B usually differs from B × A.
Determinant and inverse
For a 2×2 matrix [[a, b], [c, d]], the determinant is ad − bc and the inverse is (1/det) × [[d, −b], [−c, a]]. A matrix with determinant 0 is singular and has no inverse. Larger matrices are handled with Gaussian elimination. You can type fractions such as 1/3. This tool covers A-level Further Maths and first-year university linear algebra.
Frequently asked questions
Why can't I multiply my matrices?
The columns of A must equal the rows of B.
What does a determinant of zero mean?
The matrix is singular and cannot be inverted.
How to use the Matrix Calculator
- Enter your numbers.
- Choose the operation if needed.
- Read the answer and the working.
- Use the table below to check your understanding.
Why use this Matrix Calculator
100% in your browser
Nothing you enter is uploaded or stored.
Instant results
Updates as you type, no waiting.
Mobile friendly
Works on phones, tablets and desktops.
Light & dark mode
Follows your mfaysal.com theme.
Free, no account
No sign-up, no limits, no watermark.
Explained
Formulas, tables and sources on the page.
Matrix Calculator: chart and reference data
Source: exact arithmetic
| Operation | Requirement | Result size |
|---|---|---|
| A + B | same size | same size |
| A × B | columns of A = rows of B | rows A × cols B |
| Determinant | square | single number |
| Inverse | square, det ≠ 0 | same size |
Matrix Calculator compared with the alternatives
| Option | Shows working | Cost | Availability |
|---|---|---|---|
| This calculator | Yes | Free | Any device |
| Scientific calculator | No | £10–£20 | Needs the device |
| Spreadsheet | With formulas | Licence or account | Needs setup |
Who uses it in the UK
- GCSE and A-level revision
- University and coursework grades
- Electronics and science labs
- Sports stats and health checks
More questions
Does it show the working?
Where it helps, yes – the result section explains the steps so you can check your homework or report.
Can I use it for GCSE or A-level revision?
Yes. It is a good way to check answers, but make sure you can do the method by hand, as calculators are not allowed in every exam paper.
How accurate is it?
It uses standard double-precision arithmetic, accurate to about 15 significant figures. Results are rounded only for display.
Is my data stored?
No. Everything is calculated in your browser.
✨ New: Remove the background from any image free – private, in your browser, transparent PNG.
Related free tools
Note: This free tool runs entirely in your browser. No data is sent or stored. Results are for information only.