Easily multiply matrices online with our free Matrix Multiplication Calculator. Input your matrices, get instant results, and understand the step-by-step process of matrix multiplication.
Matrix multiplication is a fundamental operation in linear algebra that combines two matrices to produce a new matrix, known as the product matrix. The rules and procedures for performing matrix multiplication are essential for various mathematical applications.
The number of columns in the first matrix must equal the number of rows in the second matrix. If matrix A has dimensions m×n and matrix B has dimensions n×p, then the product AB will have dimensions m×p.
The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix. For example, if A is a 2×3 matrix and B is a 3×2 matrix, their product will be a 2×2 matrix.
For each element in the resulting product matrix, compute the dot product of the corresponding row from the first matrix and column from the second matrix. This involves:
For element Cij of product matrix C = AB:
Cij = Ai1×B1j + Ai2×B2j + ... + Ain×Bnj
Consider two matrices:
Matrix A:
Matrix B:
The resulting product matrix C = AB:
For example, C11 = (1×7) + (2×9) + (3×11) = 7 + 18 + 33 = 58