# Matrix multiplication

## World's simplest math tool

Free online matrix multiplicator. Just enter your matrices on the left and you'll automatically get a product of all matrices on the right. There are no ads, popups or nonsense – just a matrix multiplication calculator. Created by mathematicians for mathematicians.

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A link to this tool, including input, options and all chained tools.

Matrix multiplication tool
What is a matrix multiplication?

This tool multiplies matrices. The matrix product is calculated as sum of rows multiplied by columns. You can separate matrices with pipe symbols, star symbols or dashes. It allows you to customize input and output matrix row and column sepators. You can also specify the rounding accuracy of the product. Optionally, you can also prettify the output matrix and align all its columns for a nicer look. One last thing is that this tool supports multiplying a scalar by a matrix as well. Mathabulous!

Matrix multiplication examples
Click to use

Multiply Two Two-by-two Matrices

This example calculates the product of two 2x2 matrices.

1 2
3 4
*
9 8
7 6

23 20
55 48

**Required options**

Input matrix element separator.
(Space by default.)

Input matrix row separator.
(Newline by default.)

Result matrix element separator.
(Space by default.)

Result matrix row separator.
(Newline by default.)

Add extra spacing to align matrix columns.

Find product of 4x2 and 2x4 Matrices

This example multiplies a 4 by 2 matrix with a 2 by 4 matrix.

0.2 0.5
0.3 0.1
0.4 0.7
0.7 0.3
*
4 2 3 5
6 1 0 8

3.8 0.9 0.6 5
1.8 0.7 0.9 2.3
5.8 1.5 1.2 7.6
4.6 1.7 2.1 5.9

**Required options**

Input matrix element separator.
(Space by default.)

Input matrix row separator.
(Newline by default.)

Result matrix element separator.
(Space by default.)

Result matrix row separator.
(Newline by default.)

Add extra spacing to align matrix columns.

Automatically choose appropritate precision
for matrix multiplication.

Use Pipe as Matrix Separator

In this example we multiply three matrices and use pipe to separate first two and a star for the third matrix.

3 2 0 | 7 8 1
5 6 2 | 2 3 4
4 1 8 | 0 1 9
*
1 0 2
4 5 6
3 7 9

178 227 329
428 629 877
442 775 1038

**Required options**

Input matrix element separator.
(Space by default.)

Input matrix row separator.
(Newline by default.)

Result matrix element separator.
(Space by default.)

Result matrix row separator.
(Newline by default.)

Add extra spacing to align matrix columns.

Automatically choose appropritate precision
for matrix multiplication.

Multiply a Matrix by a Scalar

In this example we multiply a unitary matrix by two scalar values, where one scalar value is put at the beginning of matrix and second scalar value at the end.

5
*
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
*
3

15 0 0 0
0 15 0 0
0 0 15 0
0 0 0 15

**Required options**

Input matrix element separator.
(Space by default.)

Input matrix row separator.
(Newline by default.)

Result matrix element separator.
(Space by default.)

Result matrix row separator.
(Newline by default.)

Add extra spacing to align matrix columns.

Multiply Four Matrices in a Grid

In this example we multiply four 4x4 matrices that are laid out in a grid separated by pipes and dashes.

1 1 1 1 | 2 2 2 2
1 1 1 1 | 2 2 2 2
1 1 1 1 | 2 2 2 2
1 1 1 1 | 2 2 2 2
-----------------
3 3 3 3 | 4 4 4 4
3 3 3 3 | 4 4 4 4
3 3 3 3 | 4 4 4 4
3 3 3 3 | 4 4 4 4

1536 1536 1536 1536
1536 1536 1536 1536
1536 1536 1536 1536
1536 1536 1536 1536

**Required options**

Input matrix element separator.
(Space by default.)

Input matrix row separator.
(Newline by default.)

Result matrix element separator.
(Space by default.)

Result matrix row separator.
(Newline by default.)

Add extra spacing to align matrix columns.

Pro tips
Master online math tools

You can pass input to this tool via

__?input__query argument and it will automatically compute output. Here's how to type it in your browser's address bar. Click to try!
https://onlinemathtools.com/matrix-multiply

__?input__=1%202%0A3%204%0A%2A%0A9%208%0A7%206&input-element-separator=%20&input-row-separator=%5Cn&output-element-separator=%20&output-row-separator=%5Cn&prettify-matrix=true
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