Calculator for the multiplication of two matrices with dimension (m,n) and (n,j).

The multiplication of two matrices A and B requires that the number of columns of the first matrix is equal to the number of rows of the second matrix. The product obtained by multiplying the row and column elements and summed. For the first element of the result matrix, the elements of the first row of the first matrix are multiplied by the elements of the first column of the second matrix and summed. For the other elements the same for the other rows and columns.

$A\cdot B=\left(\begin{array}{cccc}{a}_{11}& {a}_{12}& \dots & {a}_{1n}\\ {a}_{21}& {a}_{22}& \dots & {a}_{2n}\\ & \vdots \\ {a}_{m1}& {a}_{m2}& \dots & {a}_{mn}\end{array}\right)\cdot \left(\begin{array}{cccc}{b}_{11}& {b}_{12}& \dots & {b}_{1j}\\ {b}_{21}& {b}_{22}& \dots & {b}_{2j}\\ & \vdots \\ {b}_{n1}& {b}_{n2}& \dots & {b}_{nj}\end{array}\right)$

Enter the matrix elements for matrix A: a_{1,1}, a_{1,2}, ..., a_{m,n}

Enter the matrix elements for matrix B: b_{1,1}, b_{1,2}, ..., b_{n,j}

The entered matrices are:

Product of the matrices:

$A\cdot B=C=\left(\begin{array}{cccc}{c}_{11}& {c}_{12}& \dots & {c}_{1j}\\ {c}_{21}& {c}_{22}& \dots & {c}_{2j}\\ & \vdots \\ {c}_{m1}& {c}_{m2}& \dots & {c}_{mj}\end{array}\right)$

Matrix multiplication elements:

Result matrix:

Here is a list of of further useful calculators:

Index Matrix Determinant Sum and dif of MxN matrices Solver Adjugate matrix Solver Inverse Matrix QR decomposition