Need help multiplying matrices for your math homework, engineering project, or linear algebra course? Our Matrix Multiplication Calculator allows you to input matrices of any compatible size and get accurate results in seconds. Whether you’re a student or professional, this tool simplifies matrix operations like a pro!
What is Matrix Multiplication?
Matrix multiplication is a fundamental operation in linear algebra where two matrices are multiplied to form a new matrix. Unlike regular multiplication, matrix multiplication involves rows and columns of numbers and follows a specific rule: the number of columns in the first matrix must equal the number of rows in the second matrix.
Matrix Multiplication Formula
If A is an m×n matrix and B is an n×p matrix, their product AB will be an m×p matrix. Each element in the resulting matrix is calculated as:
C[i][j] = Σ A[i][k] × B[k][j] (sum over k = 1 to n)
Where:
- A[i][k] = element from row i of Matrix A
- B[k][j] = element from column j of Matrix B
- C[i][j] = resulting matrix element at position (i,j)
How to Use the Matrix Multiplication Calculator
- Enter the number of rows and columns for Matrix A and Matrix B.
- Input the matrix values manually or paste them.
- Click on “Calculate” to get the matrix product.
- View step-by-step result in a clean matrix format.
Features of Our Matrix Calculator
- ✅ Supports multiplication of 2×2, 3×3, 4×4, and custom matrix sizes
- 📐 Auto-validation of dimensions for compatibility
- 📊 Step-by-step calculation breakdown
- 🖥️ Works on mobile, tablet, and desktop
- 📎 Copy or export results easily
Benefits of Using This Tool
- ⏱ Saves time for students solving matrix problems
- 🎓 Ideal for linear algebra, calculus, and engineering subjects
- 📚 Helps verify homework and exam answers
- 🧠 Assists in learning matrix multiplication step by step
Example
Matrix A (2×3):
[1 2 3] [4 5 6]
Matrix B (3×2):
[7 8] [9 10] [11 12]
Result (2×2):
[58 64] [139 154]
Common Applications of Matrix Multiplication
- 📐 Geometry transformations (rotation, scaling, translation)
- 🤖 Robotics and computer vision
- 💾 Computer graphics and 3D modeling
- 🔄 System of linear equations
- 📡 Network and graph theory analysis
Matrix Multiplication Rules Recap
- Matrix A columns = Matrix B rows
- Order matters: A × B ≠ B × A (in most cases)
- Distributive over addition: A × (B + C) = A×B + A×C
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FAQs About Matrix Multiplication Calculator
1. What matrix sizes does the calculator support?
It supports up to 10x10 matrices depending on device capability.
2. Can I multiply non-square matrices?
Yes, as long as the inner dimensions match (columns of A = rows of B).
3. Does it show steps?
Yes, it displays element-wise calculations in detail.
4. Can I use this on mobile?
Yes, the tool is responsive and mobile-friendly.
5. Is it free to use?
Yes, the matrix multiplication calculator is 100% free and doesn’t require registration.