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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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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 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
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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