# 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 math nerds from team Browserling.
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Input Matrix Options
Input matrix element separator. (Space by default.)
Input matrix row separator. (Newline by default.)
Output Matrix Options
Result matrix element separator. (Space by default.)
Result matrix row separator. (Newline by default.)
Add extra spacing to align matrix columns.
Product Accuraccy
Matrix product accuracy. (How many digits after decimal point.) (Five by default.)
Automatically choose appropritate precision for matrix multiplication.
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
These options will be used automatically if you select this example.
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
These options will be used automatically if you select this example.
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
These options will be used automatically if you select this example.
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
These options will be used automatically if you select this example.
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
These options will be used automatically if you select this example.
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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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 create a list of excessive numbers.
Quickly create a list of deficient numbers.
Quickly generate a list of perfect numbers.
Quickly create a list of slightly defective 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 find all factors of the given integer.
Quickly decompose integers into their prime factors.
Quickly find out if the given integer is a prime number.
Quickly check if the given number is a Fibonacci number
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 Heighway triangle fractal.
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 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 Koch triangle fractal.
Quickly draw a Koch n-gon fractal.
Quickly draw a quadratic Koch flake fractal.
Quickly draw a Cesaro fractal.
Quickly draw a Cesaro n-gon fractal.
Quickly draw a triflake fractal.
Quickly draw a quadric cross 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 Pythagoras tree fractal.
Quickly draw a Fibonacci word fractal.
Quickly draw an H-tree fractal.
Quickly draw a V-tree fractal.
Quickly generate a Morton Z-order fractal curve.
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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.
Calculate Pi Digit Sum
Find the sum of pi digits.
Calculate e Digit Sum
Find the sum of e digits.
Calculate Golden Ratio Digit Sum
Find the sum of Golden Ratio digits.
Generate Champernowne Digits
Generate Champernowne constant's digits.
Find n-th Champernowne Digit
Calculate the n-th digit of Champernowne constant.
Decode a Look-and-say Sequence
Perform the inverse operation on a look-and-say sequence.
Calculate p-adic expansions of arbitrary numbers.
Generate Pandigital Number Sequence
Create a list of pandigital numbers.
Generate Stanley Number Sequence
Create a list of Stanley 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 Secant Number Sequence
Create a list of secant numbers.
Generate Golomb Number Sequence
Create a list of Golomb-Silverman numbers.
Generate Euler's Totient Number Sequence
Create a list of Euler's phi numbers.
Generate Juggler Number Sequence
Create a list of juggler numbers.
Generate Lucky Number Sequence
Create a list of lucky numbers.
Generate Motzkin Number Sequence
Create a list of motzkin numbers.
Create a list of Padovan numbers.
Generate Pseudoperfect Number Sequence
Create a list of semiperfect numbers.
Generate Ulam Number Sequence
Create a list of Ulam numbers.
Generate Weird Number Sequence
Create a list of weird numbers.
Generate Superperfect Number Sequence
Create a list of superperfect numbers.
Partition a Number
Find all partitions of the given integer.
Generate Partition Number Sequence
Create a list of Partition function numbers.
Generate Arithmetic Progression
Create an arithmetic sequence of numbers.
Generate Geometric Progression
Create a geometric sequence of numbers.
Generate Polynomial Progression
Create a polynomial sequence of numbers.
Generate Natural Number Sequence
Create a list of natural numbers.
Generate Powers of Two
Create a list of numbers of powers of two.
Generate Powers of Ten
Create a list of numbers of powers of ten.
Generate a Sparse Matrix
Generate a matrix with very few non-zero elements.
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.
Given a matrix, find its adjunct.
LU Factor a Matrix
Decompose a matrix into LU factors.
Find Matrix Eigenvalues
Find eigenvalues of a matrix.
Prettify a Matrix
Beautify a matrix by neatly aligning all its columns.
Reformat a Matrix
Convert matrix in one format to another format.
Draw a Fibonacci Spiral
Generate a Fibonacci spiral curve.
Draw Fibonacci Rectangles
Generate a drawing of Fibonacci rectangles.
Generate a Padovan equiliteral triangles 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.
Draw a Gabriel's Horn
Draw a geometric figure with infinite surface area and finite volume.
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.
Analyze Numbers
Count how many times each number appears.
Rewrite a Number as a Sum
Create a sum that adds up to the given number.
Generate a Multiplication Table
Draw an n×m multiplication table.
Flip a Coin
Toss a coin and get head or tails.
Roll a Dice
Throw a dice and get a number on its side.