How to Enter Matrices and Perform Calculations on Matrix Calculator (matrixcalc.org)

Open matrixcalc.org, type your numbers into the grid cells for Matrix A (and Matrix B if needed), then click the operation button you want — or type an expression like {{1,2},{3,4}}^-1 into the input field and press Enter. The result appears below with step-by-step solutions for many operations. This works for both square and non-square matrices; leave extra cells empty to define a non-square shape.

Entering matrix elements

The site gives you two ways to get data in:

• Grid entry — Click a cell and type a number. Use ↵ Enter, Space, or the arrow keys to move between cells. Backspace and Delete clear a cell. To build a non-square matrix, just leave the unused cells empty.
• Matrix literal syntax — Type the whole matrix at once in the form {{1,2,3},{4,5,6},{7,2,9}}, where each inner {...} is a row. This is faster for anything larger than 2×2 and avoids clicking cell by cell.

You can paste a matrix from a text editor with Ctrl/Cmd + V, and you can drag a matrix from the results area back into the input (or out to a text editor).

What values are accepted

The input field is not limited to plain integers. According to the site, you can enter:

So if you need an exact fraction or a symbolic entry, you don't have to convert it to a decimal first.

Running calculations

There are two routes, and they produce the same results.

Route 1: Click an operation button

Each matrix panel (A and B) has buttons for the common operations: Determinant, Inverse, Transpose, Rank, Multiply by, Row echelon form, Diagonal matrix, To the power of, LU decomposition, Cholesky decomposition. Between the two panels you'll find the binary operations: A × B, A + B, A − B. Below that are A*X=B and A^-1 for solving systems.

Click the button, and the calculator applies that operation to the matrix you entered.

Route 2: Type an expression

Type the operation directly, using operators + - * / \ ! ^ ^{*} and functions such as:

sqrt, cbrt, exp, log, abs, conjugate, arg, min, max, gcd, rank, adjugate, inverse, determinant, transpose, pseudoinverse, trace, cos, sin, tan, cot, cosh, sinh, tanh, coth, arccos, arcsin, arctan, arccot, arcosh, arsinh, artanh, arcoth, derivative, factor, resultant

For example:

determinant({{1,2,3},{4,5,6},{7,2,9}})
{{1,2},{3,4}}^-1
{{11,3},{7,11}}*{{8,0,1},{0,3,5}}

Press Enter and the result is computed. The site lists these exact examples, so they're a safe way to confirm your syntax is right before trying something more complex.

Reading and formatting the result

• Step-by-step solutions are provided for many operations (the site advertises solution steps alongside determinant, inverse, rank, and system solving).
• Decimal vs. fraction display — There are controls for "Display decimals," "number of fraction digits," and "number of significant digits." Use these when you want an exact fraction instead of a rounded decimal, or when you need to control rounding.
• Cleaning up — The ↶ (undo) and Clean controls reset or step back through your input.

Solving systems of linear equations

For A*X = B, enter the coefficient matrix as A and the constants as B, then use the A*X=B control. The site also supports the Y+A=B form. Because the calculator handles non-square matrices (empty cells), you can set up systems that aren't square, though the solution method and whether a unique solution exists depend on the matrix itself.

Common snags

• Non-square matrices — Don't fill every cell. Empty cells are how the calculator knows the shape is rectangular rather than square.
• Syntax errors in literals — Rows go inside {...}, and the whole matrix is wrapped in another {...}: {{row1},{row2}}. A missing brace is the usual cause of a parse failure.
• Symbolic entries — Expressions like (1+x)/y^2 are accepted, but if x or y aren't defined the result stays symbolic rather than numeric.
• Keyboard navigation — If typing seems to jump cells unexpectedly, you're probably hitting Space or an arrow key, which move the cursor rather than insert a character.

Quick reference

The site also links to Wikipedia for background on matrices if you need to review the underlying concepts before computing.