Linear Algebra
Matrix Multiplication Calculator
Multiply matrices A and B to produce the product matrix AB while verifying dimensional compatibility.
Multiply compatible matrices (A · B).
4 4 10 8
Matrix product
(AB)_{ij} = Σₖ A_{ik} B_{kj}Each entry in the product is the dot product of a row of A with a column of B. The output matrix adapts to the valid shape.
How to use
- Enter matrix A and matrix B with rows separated by new lines.
- Ensure the number of columns in A equals the number of rows in B.
- Review the resulting product matrix and its size.
Example
Input: A = [[1,2],[3,4]], B = [[2,0],[1,2]]
Output: AB = [[4,4],[10,8]]
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Matrix Multiplication Calculator: matrix calculator, determinant calculator, matrix multiplication calculator, eigenvalue calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Matrix Multiplication Calculator: Performs matrix multiplication when dimensions are compatible. It's built around matrix multiplication, product, linear algebra, so you can go from a raw question to a checked answer without switching tools.
The math behind it: Each entry in the product is the dot product of a row of A with a column of B. The output matrix adapts to the valid shape. The core relationship is (AB)_{ij} = Σₖ A_{ik} B_{kj}, shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Enter matrix A and matrix B with rows separated by new lines. (2) Ensure the number of columns in A equals the number of rows in B. (3) Review the resulting product matrix and its size. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering A = [[1,2],[3,4]], B = [[2,0],[1,2]] returns AB = [[4,4],[10,8]]. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
Can I multiply non-square matrices?
Absolutely. As long as the inner dimensions match, the output size adapts to the inputs.
How are results formatted?
Results appear in a preformatted grid that you can copy into spreadsheets or documentation.
What formula does the Matrix Multiplication Calculator use?
Each entry in the product is the dot product of a row of A with a column of B. The output matrix adapts to the valid shape.
How do I use the Matrix Multiplication Calculator?
Enter matrix A and matrix B with rows separated by new lines. Ensure the number of columns in A equals the number of rows in B. Review the resulting product matrix and its size.