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Matrix Multiplication — result sheet
Multiply two finite row-major 3x3 matrices using ordered row-column dot products.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: cij = ai1 b1j + ai2 b2j + ai3 b3j for every row i and column j from 1 through 3.
The product A x B is formed by taking the dot product of each row of A with each column of B. The operation is ordered, so reversing the matrices generally changes the result even when both products are defined.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- A11 — matrix entry; Row 1, column 1 of matrix A.; minimum -1000; maximum 1000
- A12 — matrix entry; Row 1, column 2 of matrix A.; minimum -1000; maximum 1000
- A13 — matrix entry; Row 1, column 3 of matrix A.; minimum -1000; maximum 1000
- A21 — matrix entry; Row 2, column 1 of matrix A.; minimum -1000; maximum 1000
- A22 — matrix entry; Row 2, column 2 of matrix A.; minimum -1000; maximum 1000
- A23 — matrix entry; Row 2, column 3 of matrix A.; minimum -1000; maximum 1000
- A31 — matrix entry; Row 3, column 1 of matrix A.; minimum -1000; maximum 1000
- A32 — matrix entry; Row 3, column 2 of matrix A.; minimum -1000; maximum 1000
- A33 — matrix entry; Row 3, column 3 of matrix A.; minimum -1000; maximum 1000
- B11 — matrix entry; Row 1, column 1 of matrix B.; minimum -1000; maximum 1000
- B12 — matrix entry; Row 1, column 2 of matrix B.; minimum -1000; maximum 1000
- B13 — matrix entry; Row 1, column 3 of matrix B.; minimum -1000; maximum 1000
- B21 — matrix entry; Row 2, column 1 of matrix B.; minimum -1000; maximum 1000
- B22 — matrix entry; Row 2, column 2 of matrix B.; minimum -1000; maximum 1000
- B23 — matrix entry; Row 2, column 3 of matrix B.; minimum -1000; maximum 1000
- B31 — matrix entry; Row 3, column 1 of matrix B.; minimum -1000; maximum 1000
- B32 — matrix entry; Row 3, column 2 of matrix B.; minimum -1000; maximum 1000
- B33 — matrix entry; Row 3, column 3 of matrix B.; minimum -1000; maximum 1000
Worked example
| Input | Value |
|---|---|
| A11 | 1 |
| A12 | 2 |
| A13 | 3 |
| A21 | 0 |
| A22 | 1 |
| A23 | 4 |
| A31 | 5 |
| A32 | 6 |
| A33 | 0 |
| B11 | 2 |
| B12 | 0 |
| B13 | 1 |
| B21 | 1 |
| B22 | 3 |
| B23 | 0 |
| B31 | 0 |
| B32 | 2 |
| B33 | 1 |
A x B = [[4, 12, 4], [1, 11, 4], [16, 18, 5]].
Assumptions and limits
- A and B are finite real 3x3 matrices in fixed row-major key order.
- Each entry is bounded inclusively from -1000 through 1000 and every intermediate product and sum must remain within finite arithmetic.
- The product is ordinary ordered matrix multiplication; no elementwise product, transpose, unit conversion, or symbolic parsing is performed.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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