Matrix Multiplication Calculator
Perform matrix multiplication effortlessly. Enter your matrices and get the product instantly.
Matrix A
Matrix B
Result:
Result Matrix (C = A x B):
Result:
Enter matrix values and calculate to see the result here.
Understanding Matrix Multiplication
Matrix multiplication is a fundamental operation in linear algebra, combining two matrices to produce a new matrix. For matrix multiplication of A and B to be defined, the number of columns in A must equal the number of rows in B. If A is an m×n matrix and B is an n×p matrix, their product C will be an m×p matrix.
Each element \( C_{ij} \) in the resulting matrix C is calculated as the sum of the products of corresponding elements from the i-th row of matrix A and the j-th column of matrix B. Mathematically, it's represented as: $$ C_{ij} = \sum_{k=1}^{n} A_{ik} \times B_{kj} $$
This calculator helps you perform this operation quickly and accurately, whether you're working on linear transformations, solving systems of equations, or in computer graphics. Use it to simplify complex calculations and enhance your understanding of matrix operations.