# 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.

announcement
heads up!

We just launched a new site — Online UTF8 Tools — utilities for working with UTF8 encoding. Check it out!

*fullscreen*

*fullscreen_exit*

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 2x4 and 4x2 Matrices

This example multiplies a 2 by 4 matrix with a 4 by 2 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
All math tools

Quickly visualize rules of an Lindenmayer rewrite system.

Quickly generate a list of primes.

Quickly generate a list of Fibonacci numbers.

Quickly generate a list of extended, negative Fibonacci numbers.

Quickly generate a list of Fibonacci primes.

Quickly generate a list of Fibonacci words.

Quickly generate a list of Tribonacci words.

Quickly generate a list of Lucas numbers.

Quickly generate a list of extended, negative Lucas numbers.

Quickly generate a list of Lucas numbers that are also prime numbers.

Quickly generate a list of perfect numbers.

Quickly generate random numbers.

Quickly generate a list of look-and-say sequence numbers.

Quickly create a list of Prouhet-Thue-Morse sequence values.

Quickly create a list of dragon curve sequence values.

Quickly create a list of Oldenburger-Kolakoski sequence values.

Quickly create a list of Gijswijt sequence values.

Quickly create a list of Golay-Rudin-Shapiro sequence values.

Quickly create a list of Baum-Sweet sequence values.

Quickly create a list of Moser-de Bruijn sequence values.

Quickly generate a list of even numbers.

Quickly generate a list of odd numbers.

Quickly generate π constant's digits to arbitrary precision.

Quickly calculate Euler constant's digits to arbitrary precision.

Quickly calculate φ constant's digits to arbitrary precision.

Quickly calculate factorials.

Quickly create a triangluar array of binomial coefficients.

Quickly create a matrix with random elements.

Quickly create a unit matrix with ones along the diagonal.

Quickly find the transpose of a matrix.

Quickly find the inverse of a matrix.

Quickly calculate the determinant of a matrix.

Quickly find the sum of two or more matrices.

Find the difference of two or more matrices.

Quickly find the product of matrices.

Quickly draw a Hilbert space-filling curve.

Quickly draw a Harter-Heighway space-filling dragon fractal.

Quickly draw a Davis-Knuth dragon fractal.

Quickly draw a triple dragon fractal.

Quickly draw a quaddragon fractal.

Quickly draw a hexdragon curve.

Quickly draw a Peano space-filling fractal.

Quickly draw a Moore space-filling curve.

Quickly draw a Peano-Gosper space-filling curve.

Quickly draw a Sierpinski arrowhead fractal curve.

Quickly draw a Sierpinski sieve fractal.

Quickly draw a Sierpinski closed plane fractal curve.

Quickly draw a Sierpinski carpet fractal.

Quickly draw a Sierpinski maze fractal.

Quickly draw a Sierpinski square fractal.

Quickly draw a Sierpinski pentaflake fractal.

Quickly draw a Sierpinski hexaflake fractal.

Quickly draw a Sierpinski n-gon fractal.

Quickly draw a Koch island fractal curve.

Quickly draw a Koch antisnowflake fractal.

Quickly draw a triflake fractal.

Quickly draw a quadratic Koch flake fractal.

Quickly draw a quadric cross fractal.

Quickly draw a Cesaro fractal.

Quickly draw a self-similar Levy C fractal curve.

Quickly draw a Vicsek snowflake fractal.

Quickly draw a T-square fractal.

Quickly draw a Cantor set fractal.

Quickly draw an asymmetric Cantor set fractal.

Quickly draw a generalized Cantor set fractal.

Quickly draw an ε-Cantor set fractal.

Quickly draw a Cantor dust fractal.

Quickly draw a Fibonacci word fractal.

Quickly draw an H-tree fractal.

Quickly generate a Morton Z-order fractal curve.

Coming soon
These math tools are on the way

Find n-th e Digit

Calculate the n-th digit of Euler's number.

Find n-th Golden Ratio Digit

Calculate the n-th digit of Golden Ratio.

Find n-th Pi Digit

Calculate the n-th digit of pi constant.

Find Prime Factors

Given a number, factorize it and find its prime factors.

Test if a Number is a Prime

Find out if the given number is a prime number.

Test if a Number is a Fibonacci Number

Find out if the given number is a Fibonacci number.

Decode a Look-and-say Sequence

Perform the inverse operation on a look-and-say sequence.

Generate Abundant Number Sequence

Create a list of excessive numbers.

Generate Bell Number Sequence

Create a list of Bell numbers.

Generate Carmichael Number Sequence

Create a list of Charmichel numbers.

Generate Catalan Number Sequence

Create a list of Catalan numbers.

Generate Composite Number Sequence

Create a list of composite numbers.

Generate Deficient Number Sequence

Create a list of deficient numbers.

Generate Secant Number Sequence

Create a list of secant numbers.

Multiply a Matrix by a Scalar

Multiply all matrix elements by a number.

Check if a Matrix is Singular

Determine if a matrix is degenerate.

Find the Co-factor Matrix

Given a matrix, find its cofactor matrix.

Find the Adjugate Matrix

Given a matrix, find its adjunct.

LU Factor a Matrix

Decompose a matrix into LU factors.

Find Matrix Eigenvalues

Find eigenvalues of a matrix.

Draw a Apollonian Gasket

Generate an Apollonian gasket fractal.

Draw a Mandelbrot Fractal

Generate a Mandelbrot fractal.

Draw a Julia Fractal

Generate a Julia fractal.

Draw a Rauzy Fractal

Generate a Rauzy fractal.

Draw Blancmange Fractal Curve

Generate a Blancmange fractal.

Draw Weierstrass Function

Generate a Weierstrass fractal.

Draw Minkowski Question-mark Curve

Generate a Minkowski Question-mark fractal.

Draw Thomae's Function

Generate a Thomae's function (also known as popcorn or raindrop function).

Draw Dirichlet's Function

Generate a Dirichlet's function.

Convert Words to Numbers

Convert numbers as English text to actual digits.

Convert Numbers to Words

Convert numbers to written English text.

Convert Decimal Notation to Scientific Notation

Convert numbers written in decimal form to scientific form.

Convert Scientific Notation to Decimal Notation

Convert numbers written in scientific form to decimal form.

Round Numbers Up

Apply ceil operation to numbers.

Round Numbers Down

Apply floor operation to numbers.

Subscribe!
Never miss an update

Cool!

Notifications
We'll let you know when we add this tool

Cool!