What This Tool Does
Use this browser-based calculator for A + B, A − B, A × B, AT, determinant, inverse, rank, and Solve Ax = b. It accepts signed numbers, decimals, and simple fractions, uses exact fraction arithmetic, and displays the calculation steps. Matrices can be up to 6 × 6.
Set Matrix Dimensions
Choose an operation first. The dimension controls then match its requirements:
- Square modes force Cols for Matrix A to equal Rows.
- Add / Subtract makes Matrix B the same size as A and disables B's dimension inputs.
- Multiply sets B's rows to A's columns. Choose B's Cols.
- Solve Ax = b uses square A and shows Vector b with one value per row. It has no separate B dimension controls.
Changing the operation or dimensions rebuilds the input grids and hides the previous result.
Calculate a Result
- Enter a number such as
-3or2.5, or a fraction such as3/4, in every generated cell. - For Add / Subtract, choose A + B or A − B.
- Click Calculate to show the result and the page's Steps list.
- Click Reset to rebuild the current grids and clear the result and error. It keeps the selected operation and does not explicitly restore the default dimensions.
- Use Copy result or Download result (.txt) to save the result summary. These controls do not include the rendered Steps list.
Supported Operations and Requirements
- Addition and subtraction: A and B must have matching dimensions.
- Multiplication: A's columns must equal B's rows.
- Transpose: works on Matrix A and swaps its rows and columns.
- Determinant, inverse, and rank: require square Matrix A.
- Inverse: requires a non-singular matrix.
- Solve Ax = b: requires square A. The result can be a unique solution, infinitely many solutions, or no solution when the system is inconsistent.
The determinant and inverse use row elimination. Rank reduces A to reduced row echelon form and counts pivot columns. Solving reduces the augmented matrix [A | b] to reduced row echelon form.
Validation, Exact Results, and Limits
The maximum size is 6 × 6. Empty cells and fractions with a zero denominator produce validation errors before calculation. Variables, expressions, and other unsupported symbols are rejected; cells are not executed as code.
Values and intermediate calculations use exact fractions, reduced to lowest terms. Matrix results are shown as exact fractions. Determinant statistics and unique Solve Ax = b values may also show a decimal approximation. Singular matrices cannot be inverted, and inconsistent systems cannot produce a unique solution.
Privacy and Processing
The calculator parses and processes matrix values in your browser and does not send those matrix values as part of its calculation workflow. The page also has a separate subscription form that posts an email address to /assets/subscribe.php.
Frequently Asked Questions
What matrix operations does this calculator support?
Addition, subtraction, multiplication, and transpose of matrices, plus determinant, inverse, and rank of a single matrix, and solving a linear system Ax = b. Each is a separate mode of the same tool.
What size matrices can I use?
Any matrix from 1x1 up to 6x6. Larger matrices are not supported.
How are results kept exact?
Every entry is stored as an exact fraction (an integer numerator and denominator, reduced to lowest terms), not a floating-point decimal. Results such as 1/3 or 7/12 stay exact. Determinant statistics and unique Solve Ax = b values may also include a decimal approximation.
How does it detect a singular matrix?
During row elimination, if a column has no nonzero entry available for a pivot, the matrix is reported as singular: the determinant is exactly 0 and no inverse exists. Exact arithmetic makes this detection exact, not an approximation. The tool does not evaluate general numerical conditioning.
Does the calculator execute my input as code?
No. Each matrix cell accepts a plain number or a simple fraction such as 3/4. A fixed parser rejects other expressions or symbols; nothing you enter is evaluated as code.