What is the Matrix Multiplication Calculator?
The matrix multiplication calculator is a free online tool that helps you work out matrix multiplication quickly and accurately. It uses the standard formula Standard matrix multiplication (columns of A must equal rows of B) and shows the result instantly as you type, along with a full breakdown so you can see exactly how the answer was reached.
How to use this calculator
- Enter matrix A with rows separated by ; and numbers by spaces.
- Enter matrix B.
- See the product.
Formula used
Standard matrix multiplication (columns of A must equal rows of B)Explanation of each input
- Matrix A (rows separated by ;) โ the matrix a (rows separated by ;) used in the calculation.
- Matrix B (rows separated by ;) โ the matrix b (rows separated by ;) used in the calculation.
Understanding your result
- Product A x B โ the calculated product a x b.
Step-by-step calculation
For the example values [[1,2],[3,4]] x [[5,6],[7,8]]:
- Apply the formula:
Standard matrix multiplication (columns of A must equal rows of B) - Substitute the values: row-by-column
- Result: [[19,22],[43,50]]
Worked example
| Inputs | [[1,2],[3,4]] x [[5,6],[7,8]] |
|---|---|
| Working | row-by-column |
| Result | [[19,22],[43,50]] |
Benefits and practical uses
This calculator saves you time and reduces errors when you need matrix multiplication. It is useful for students, professionals and anyone who wants a fast, reliable answer without manual calculation. Results update instantly, work in your browser and can be copied or shared in one click.
Assumptions and limitations
- Compatible dimensions.
Frequently asked questions
When can two matrices be multiplied?
When the number of columns in A equals the number of rows in B.