Matrix Multiplication Calculator – Multiply Two Matrices
Multiply two matrices together
Table of Contents
How to Use
- Select matrix size (2x2 or 3x3)
- Enter the elements of Matrix A
- Enter the elements of Matrix B
- Click calculate to see the product matrix
What is Matrix Multiplication?
Matrix multiplication is a binary operation that produces a matrix from two matrices. Unlike element-wise multiplication, matrix multiplication follows specific rules where each element of the result is computed as the dot product of a row from the first matrix and a column from the second matrix.
How Matrix Multiplication Works
For matrices A and B, the element at position (i,j) in the result C is calculated as: C[i][j] = A[i][1]×B[1][j] + A[i][2]×B[2][j] + ... This is the sum of products of corresponding elements from row i of A and column j of B.
Properties of Matrix Multiplication
- Not commutative: A × B ≠ B × A in general
- Associative: (A × B) × C = A × (B × C)
- Distributive: A × (B + C) = A × B + A × C
- Identity matrix: A × I = I × A = A
Applications
- Computer graphics and 3D transformations
- Solving systems of linear equations
- Machine learning and neural networks
- Physics simulations and engineering
- Economics and network analysis
Frequently Asked Questions
- Is matrix multiplication commutative?
- No, matrix multiplication is not commutative. In general, A × B ≠ B × A. The order of multiplication matters and can produce completely different results.
- When can two matrices be multiplied?
- Two matrices can be multiplied when the number of columns in the first matrix equals the number of rows in the second matrix. For square matrices of the same size (like 2x2 or 3x3), multiplication is always possible.
- What is the identity matrix?
- The identity matrix is a square matrix with 1s on the main diagonal and 0s elsewhere. When any matrix is multiplied by the identity matrix, the result is the original matrix unchanged.