# Inverse Matrix Calculator

## World's Simplest Number Tool

Quickly find the inverse of a matrix in your browser. To get the inverse, just enter your matrix in the input field, optionally adjust the row and column separators in the options below, and this utility will instantly compute the inverse of your matrix. Created by developers from team Browserling.

Tool Options

#### Input Matrix Delimiter

Element delimiter of the input
matrix. (By default a space.)
Row delimiter of the input
matrix. (By default a newline.)

#### Inverse Matrix Delimiter

Element delimiter of the output
matrix. (By default a space.)
Row delimiter of the output
matrix. (By default a newline.)

#### Inverted Matrix Accuracy

Number of digits in the fractional
part. (By default five.)
Determine the precision
automatically.
Align row elements in the
invented matrix automatically.

## What Is an Inverse Matrix Calculator?

This is an online browser-based utility for finding the inverse of a matrix. The inverse matrix A-1 of a matrix A is such that the product AxA-1 is equal to the identity matrix. The result of multiplying the matrix by its inverse is commutative, meaning that it doesn't depend on the order of multiplication – A-1xA is equal to AxA-1. The inverse matrix exists only for square matrices and it's unique. The matrix has the inverse if and only if it is invertible. An invertible matrix is also sometimes called nonsingular or nondegenerate. The key property of an invertible matrix is that its determinant isn't equal to zero. In this tool, we use the Gaussian elimination method to calculate the inverse matrix. This method is very fast and here's how it works. We append the unit matrix of the same dimensions on the left side of the given matrix, and then by using elementary transformations, we bring the original matrix to the unit form. At the same time, we apply all the same elementary transformations to the unit matrix on the left side. When completed, the right side now contains the inverted matrix. With this tool, you can calculate the inverse for a matrix of any size. You can also adjust the properties and format of the inverted matrix by customizing its numerical accuracy, row and column separators, as well as how elements are aligned. That's numberwang!

## Inverse Matrix Calculator Examples

Click to try!
click me

### Inverse of a Square Matrix

In this example, we calculate the inverse of a 3 by 3 matrix containing integers. By multiplying these matrices together in any order, you'll always get the identity matrix.

2 1 3 3 3 4 5 2 8
16 -2 -5 -4 1 1 -9 1 3
Required options
These options will be used automatically if you select this example.
Element delimiter of the input
matrix. (By default a space.)
Row delimiter of the input
matrix. (By default a newline.)
Element delimiter of the output
matrix. (By default a space.)
Row delimiter of the output
matrix. (By default a newline.)
Align row elements in the
invented matrix automatically.
click me

### Custom Precision Example

In this example, we find the inverse of a matrix with dimensions 4 by 4. The resulting matrix consists of fractional numbers, so we adjust its accuracy to 3 digits after the decimal point.

2 3 6 5 -2 5 -1 3 -8 0 -7 -2 -5 -4 2 1
-1.092 1.031 -0.949 0.469 1.684 -1.561 1.398 -0.939 2.061 -2.02 1.633 -0.98 -2.847 2.949 -2.418 1.551
Required options
These options will be used automatically if you select this example.
Element delimiter of the input
matrix. (By default a space.)
Row delimiter of the input
matrix. (By default a newline.)
Element delimiter of the output
matrix. (By default a space.)
Row delimiter of the output
matrix. (By default a newline.)
Number of digits in the fractional
part. (By default five.)
Determine the precision
automatically.
Align row elements in the
invented matrix automatically.
click me

### Auto-accuracy Example

In this example, we compute the inverse of a matrix with size 10x10. We activate two automatic functions here. First, the tool determines the best accuracy of each number in the inverse matrix, and second, it adds as many spaces around numbers so that all elements align in beautiful columns.

6 6 9 5 6 4 7 4 1 2 2 9 6 3 8 1 5 6 3 5 2 3 3 9 1 9 9 0 5 4 4 0 6 2 4 7 4 1 3 0 7 9 4 3 2 4 4 7 0 8 4 3 7 3 2 0 7 1 5 2 3 7 9 6 1 1 7 9 4 4 9 2 2 2 9 2 2 4 5 4 6 7 2 3 9 4 2 7 7 8 8 0 8 8 4 0 5 7 1 0
0.27 -0.26 -0.02 -0.14 -0.03 -0.03 0.1 0.14 0.02 -0.11 0.64 -0.41 -0.02 -0.32 -0.2 -0.13 0.24 0.07 0.19 -0.28 -0.09 0.03 -0.12 0.16 0.08 0.27 -0.3 -0.49 0.32 0.24 0.23 -0.18 0.01 -0.17 -0.09 0.06 -0.14 -0.31 0.35 0.14 -0.13 0.22 0.02 0.07 0.01 -0.01 -0.11 0.03 -0.07 0.07 0.06 -0.06 0.02 0.08 -0.01 -0.11 0.07 0.03 -0.01 -0.07 -0.35 0.36 0.14 0.1 0.09 -0.14 0.22 0.56 -0.65 -0.14 -0.18 0.13 0.04 0.08 0.01 -0.23 0.27 0.34 -0.31 -0.09 0.23 -0.26 -0.02 -0.11 -0.16 0.01 0.17 0.03 0.18 -0.14 -0.67 0.43 -0.02 0.3 0.32 0.34 -0.51 -0.44 0.1 0.4
Required options
These options will be used automatically if you select this example.
Element delimiter of the input
matrix. (By default a space.)
Row delimiter of the input
matrix. (By default a newline.)
Element delimiter of the output
matrix. (By default a space.)
Row delimiter of the output
matrix. (By default a newline.)
Determine the precision
automatically.
Align row elements in the
invented matrix automatically.

### Pro tipsMaster online number 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://onlinetools.com/number/find-matrix-inverse?input=2%201%203%0A3%203%204%0A5%202%208&input-element-separator=%20&input-row-separator=%255Cn&output-element-separator=%20&output-row-separator=%255Cn&prettify-matrix=true

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