Matrix Multiplication Calculator
This calculator helps you multiply two matrices of compatible dimensions step-by-step. It is perfect for students, engineers, and professionals working with linear algebra, simplifying manual calculations and minimizing errors.
Matrix Multiplication Solver
Matrix Multiplication Formula
Where:
- $$C_{ij}$$ is the element in row i, column j of the product matrix
- $$A_{ik}$$ is the element in row i, column k of matrix A
- $$B_{kj}$$ is the element in row k, column j of matrix B
- $$n$$ is the shared dimension
This formula computes each element of the resulting matrix by summing the products of corresponding elements from the rows of matrix A and columns of matrix B.
Matrix Multiplication – Calculation Example
$$A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$
$$B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}$$
$$C = A \times B = \begin{bmatrix} (1 \cdot 5 + 2 \cdot 7) & (1 \cdot 6 + 2 \cdot 8) \\ (3 \cdot 5 + 4 \cdot 7) & (3 \cdot 6 + 4 \cdot 8) \end{bmatrix} = \begin{bmatrix} 19 & 22 \\ 43 & 50 \end{bmatrix}$$
Matrix multiplication is widely used in linear algebra, computer graphics, machine learning, and physics. The operation combines two matrices where the number of columns in the first equals the number of rows in the second. Our calculator ensures accuracy and saves time when working with large matrices.