# Matrix Multiplication Calculator

Perform matrix multiplication by entering the elements of two matrices. The calculator will compute the product matrix.

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### Using the calculator

Enter the elements of Matrix A and Matrix B in the respective text fields, separating the elements by spaces and new lines. The calculator will compute the matrix product and display the result.

### Matrix Multiplication

The calculator performs matrix multiplication of two matrices, A and B. The product matrix, C, is obtained by multiplying the corresponding elements of the matrices as follows:

The matrixes and are defined as:

.

,

To compute each element of the product matrix, we take the dot product of the i-th row of matrix A and the j-th column of matrix B. The dot product is obtained by summing the products of corresponding elements:

- the summation is taken over the common dimension (r = 1 to n).

The dimensions of the matrices must satisfy (n × m)(m × p) = (n × p) for matrix multiplication to be defined.

Please note that matrix multiplication is not commutative, except when both matrices are diagonal and have the same dimension.

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