Matrix Multiplication Calculator

Lets first understand, what is matrix multiplication and how we can find the product of two matrices?

Definition: A matrix is an ordered rectangular array of numbers or functions. The numbers or functions are called the elements or the entries of the matrix.

A matrix having m rows and n columns is called a matrix of order m × n or simply m × n matrix (read as an m by n matrix).

We denote matrices by capital letters. Some examples of matrices:

\[ A=\begin{bmatrix} a & b & c \\ d & e & f\end{bmatrix},B=\begin{bmatrix} g & h \\ i & j \\ k & l \end{bmatrix} \] \[ C= \begin{bmatrix} m & n & o \\ p & q & r \\ s & t & u \end{bmatrix} \]

Multiplication of matrices

\[ A=\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix},B=\begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix} \] \[ AB= \begin{bmatrix} 22 & 28 \\ 49 & 64 \end{bmatrix} \] \[ BA= \begin{bmatrix} 9 & 12 & 15 \\ 19 & 26 & 33 \\ 29 & 40 & 51 \end{bmatrix} \]

Note:

1. The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. Let A = [a_ij] be an m × n matrix and B = [b_jk] be an n × p matrix. Then the product of the matrices A and B is the matrix C of order m × p.

2. If AB and BA are both defined, it is not necessary that AB = BA.

For calculating the product of matrices using above matrix multiplication calculator, you have to first set the order of matrix, then enter the matrix and press confirm button, after that choose the operation, then you will get the resultant matrix in the Result section.

For element wise product of matrices, use A.B button.