The Matrix Multiplication Calculator allows you to multiply two matrices online and view the result instantly. Whether you're a student learning linear algebra or an engineer solving real-world problems, this tool simplifies complex matrix math.
How to Use the Matrix Multiplication Calculator
Follow these steps:
- Select the number of rows and columns for both matrices
- Enter each element in the matrix fields
- Click "Calculate" to get the product of the two matrices
The tool displays the resulting matrix and also highlights the step-by-step multiplication process for better understanding.
Matrix Multiplication Formula
To multiply Matrix A (m × n) and Matrix B (n × p), the resulting Matrix C will be (m × p). Each element of C is calculated as:
Cij = Σ Aik × Bkj
Example
Matrix A:
[ [1, 2], [3, 4] ]
Matrix B:
[ [5, 6], [7, 8] ]
Result:
[ [(1×5 + 2×7), (1×6 + 2×8)] = [19, 22],
[(3×5 + 4×7), (3×6 + 4×8)] = [43, 50] ]
Common Use Cases
- Solving linear algebra equations
- Computer graphics and 3D transformations
- Engineering and physics simulations
- Data science and machine learning
- School and college math assignments
Why Use a Matrix Calculator?
Manual matrix multiplication is time-consuming and error-prone. This calculator provides quick, step-by-step results, helping you save time and avoid mistakes — perfect for academic and professional use.
Frequently Asked Questions (FAQs)
What matrix sizes are supported?
You can multiply any valid matrix combination (e.g., 2×3 with 3×2, 3×3 with 3×3, etc.).
Can this calculator handle large matrices?
Yes, but larger matrices may take more time and browser memory. It's best for academic sizes up to 5x5.
Do I need to enter all matrix values manually?
Yes, just fill in the values for each element and the tool computes automatically.
Can I use it for matrix chain multiplication?
No, this tool is for direct multiplication of two matrices only.
What if dimensions are not compatible?
The tool will show an error if the number of columns in Matrix A ≠ number of rows in Matrix B.