Matrix Multiplication Calculator
Multiply two small matrices and inspect the exact row-by-column arithmetic for every result cell.
Private calculation: matrix values stay in this tab. This tool does not put dimensions, cell counts, values, results, or copied text in the URL, storage, cookies, network requests, or analytics. Analytics receives only fixed tool, action, error, or related-link identifiers.
Set compatible matrix dimensions
For A × B, Matrix A's columns must equal Matrix B's rows. If A is 2 × 3 and B is 3 × 2, the product is 2 × 2. The first outer dimension supplies the result rows, and the second outer dimension supplies its columns.
Read each row-by-column step
Each result cell is a dot product. The calculator multiplies the entries in one row of A by the matching entries in one column of B, then adds those products. For the included 2 × 3 by 3 × 2 example, the first cell is (1 × 7) + (2 × 9) + (3 × 11) = 7 + 18 + 33 = 58.
Keep fractions exact
Inputs are parsed as exact reduced rational numbers. Integers, terminating decimals such as 1.25, and simple fractions such as -3/4 never pass through binary floating-point arithmetic. Results and working keep the reduced fraction. A secondary decimal is shown to at most 10 places and carries an approximation mark when it repeats or is rounded.
Strict limits prevent ambiguous results
Every dimension is limited to 1 through 6, each raw cell to 40 characters, and the combined input to 2,880 characters. Blank cells are errors rather than implicit zeroes. Unsupported expressions, scientific notation, mixed numbers, variables, and zero denominators stop the calculation with a specific field message. Intermediate numerators and denominators also have a fixed digit limit.
Focused two-matrix scope
This calculator performs one ordered multiplication of two matrices. It does not solve matrix equations, evaluate variables, calculate determinants or inverses, chain a third matrix, import files, export documents, save history, or share values through a link. Copy result and steps includes a plain tab-separated product followed by the row-by-column work.
Frequently asked questions
How do I multiply two matrices?
Choose the rows and columns for Matrix A and Matrix B. The number of columns in A must equal the number of rows in B. Enter every cell, then select Multiply matrices. The result has A's row count and B's column count.
Can I use fractions and decimals?
Yes. Each cell accepts an ASCII integer, a terminating decimal, or a simple fraction such as -3/4. The calculator keeps exact reduced rational values through every product and sum, then adds a decimal display limited to 10 places.
Why are my matrix dimensions incompatible?
Matrix multiplication A × B is defined only when A's column count equals B's row count. The calculator marks both inner dimension controls and focuses the error summary when they differ.
Does matrix order matter?
Yes. In general, A × B and B × A are different, and reversing the order may make the dimensions incompatible. This page calculates only the displayed A × B order.
Are my matrix values uploaded or saved?
No. Calculation runs in this browser tab. The page does not put dimensions, cell counts, values, results, or copy text in URLs, storage, cookies, network requests, or analytics.