Matrix Product Calculator
Example Data Table
| Matrix A | Matrix B | Indicated Product | Result |
|---|---|---|---|
| 1 2 3 4 5 6 |
7 8 9 10 11 12 |
A × B | 58 64 139 154 |
| 2 1 0 3 |
4 | 4A | 8 4 0 12 |
| 1 2 3 4 |
n = 2 | A² | 7 10 15 22 |
Formula Used
For two matrices, the product is C = AB.
Each entry is found with this rule:
cij = ai1b1j + ai2b2j + ... + ainbnj
The number of columns in A must equal rows in B.
For scalar multiplication, each entry becomes k × aij.
For powers, An means A multiplied by itself n times.
How To Use This Calculator
- Enter Matrix A with one row per line.
- Enter Matrix B when using A × B.
- Select scalar or power mode when needed.
- Use transpose options for indicated products.
- Set decimal places for rounded output.
- Press the compute button.
- Review the result above the form.
- Download CSV or PDF when needed.
Matrix Product Calculator Guide
Matrix Product Calculator Guide
Matrix products appear in algebra, physics, graphics, economics, and data work. A product is not made by matching positions only. Each entry uses a row from the first matrix and a column from the second matrix. That rule makes dimension checking very important. This calculator checks that rule before any product is shown.
Why Matrix Order Matters
Matrix multiplication is ordered. In many cases, AB is not the same as BA. The first matrix controls the row count of the result. The second matrix controls the column count of the result. If A is 2 by 3 and B is 3 by 2, the result is 2 by 2. If the inner sizes do not match, the product is undefined.
Advanced Options
The tool supports standard products, scalar products, and powers. You can also transpose input matrices before multiplication. This helps when a question asks for A transpose times B. Rounding keeps answers readable. Fractions may be entered as values like 3/4. Decimal values are also accepted.
Checking Your Work
Use the example table before entering a large problem. Confirm each row has the same number of values. Use commas, spaces, semicolons, or new lines. Keep matrices rectangular. After submission, review the dimension report first. Then compare one entry by hand. Multiply the first row by the first column. Add the products. This confirms the method.
Study And Reporting Uses
Matrix products support transformations, systems of equations, weighted scores, and network models. A clean export is useful for assignments and reports. The CSV option saves the result for spreadsheets. The PDF option creates a quick printable record. The calculator is still a learning aid. It should not replace understanding. Always read the formula section. It explains why each entry appears. This makes mistakes easier to find.
Good Input Habits
Large matrices can hide small errors. Place one row on each line. Do not mix missing cells with zeros. A blank cell means the row is broken. A zero means a real value. Label matrices before saving exports. This helps you understand old results. Recheck signs when using negative entries. One wrong sign can change many product entries. It also helps during tests and review sessions later.
FAQs
What is an indicated product matrix?
It is a matrix operation requested by a problem. It may be A × B, BA, kA, A squared, or a transpose product. The calculator follows the chosen instruction.
Why does matrix order matter?
Matrix multiplication is not usually commutative. AB can differ from BA. The row and column order changes the calculation and may also change the final dimensions.
When is A × B possible?
A × B is possible when the number of columns in A equals the number of rows in B. Otherwise, the product is undefined.
Can I enter fractions?
Yes. You can enter values like 1/2, -3/4, or 5/8. The calculator converts them into decimal values for calculation and output.
Can this calculator square a matrix?
Yes. Select the power option and enter n = 2. The matrix must be square. Only square matrices can be multiplied by themselves.
What does transpose mean?
A transpose swaps rows and columns. The first row becomes the first column. This is useful for products like A transpose times B.
Why are decimal places included?
Decimal places control rounding. They make long decimal answers easier to read. Use more places when precision matters.
What do the export buttons do?
The CSV button saves the result for spreadsheets. The PDF button saves a printable report with the matrix product result.