Matrix Calculator

All tools

Compute the determinant, inverse, transpose, sum or product of 2×2 and 3×3 matrices. Edit the grid and see the result instantly. Free and easy to use.

Result
–
Determinant of A –
Determinant and inverse use cofactor expansion. A matrix has no inverse when its determinant is zero (a singular matrix).

About Matrix Calculator

The matrix calculator handles the operations that come up most often in linear algebra classes: determinant, inverse, transpose, matrix addition (A + B) and matrix multiplication (A × B), for both 2×2 and 3×3 matrices. Edit the grid cells and the result updates instantly.

The determinant and inverse are computed by cofactor expansion, the same method taught in textbooks. If the determinant works out to zero, the tool flags the matrix as singular — not invertible — instead of showing a misleading answer.

It is useful for checking homework, verifying a hand calculation or exploring how operations behave. The calculator is free, needs no signup and runs fully in your browser, so you can experiment as much as you like.

How to use Matrix Calculator

  1. Pick the matrix size: 2×2 or 3×3.
  2. Choose an operation: determinant, inverse, transpose, A + B or A × B.
  3. Fill in the cells of matrix A (and matrix B for addition or multiplication).
  4. Read the result — a scalar for the determinant, or a full result matrix otherwise.
  5. Click “Reset to example” anytime to restore sample values.

Frequently asked questions

A matrix has an inverse only when its determinant is nonzero. If cofactor expansion gives a determinant of 0, the matrix is singular and no inverse exists — the tool reports this explicitly.

Yes. Matrix multiplication is not commutative, so A × B usually differs from B × A. This tool computes A × B; to get the other product, swap the values between the two grids.

By cofactor expansion. For a 2×2 matrix it is ad − bc; for a 3×3 matrix the tool expands along a row, combining each entry with the determinant of its 2×2 minor.

It flips the matrix across its main diagonal, turning rows into columns. Entry (i, j) moves to position (j, i). The transpose always exists, whatever the values.

The tool focuses on 2×2 and 3×3 matrices, which cover most coursework and quick checks. Larger sizes are not supported here.
Share this
Related Tools
Percentage Calculator Answer every percentage question — X% of Y, what percent, percentage change, increase/decrease, tips and discounts. Free, in your browser. Free
Scientific Calculator A full scientific calculator with trigonometry, logarithms, powers, roots, factorials, memory and history — in degrees or radians. Free, in your browser. Free
Text to Binary, Octal & Hex Convert text to binary, octal, decimal and hexadecimal — and back again. Every field is live and editable, with delimiter, padding and uppercase options. Free
Fraction Calculator Add, subtract, multiply or divide two fractions and instantly get the simplified result, plus its decimal, mixed-number and percentage forms. Free and instant. Free
Average Calculator Paste a list of numbers to instantly get the mean, median, mode, range, sum, count and more. Robust parsing handles commas, spaces and new lines. Free and instant. Free
Standard Deviation Calculator Enter a data set to compute the sample and population standard deviation, variance and mean. Robust parsing handles commas, spaces and new lines. Free and instant. Free
Need help?
Found an issue with this tool? Let our team know.
Report an issue

Add this free tool to your own website — copy and paste the code below.