## Summary

The Excel MUNIT function returns a unit matrix for a given dimension, n, with a size of n x n. This resulting matrix contains ones on the main diagonal and zeros in every other position.

## Purpose

Return unit matrix for a given dimension

## Return value

Unix matrix of size n x n

## Syntax

``=MUNIT(dimension)``
• dimension - An integer for the size of the unit matrix.

## How to use

The MUNIT function returns a unit matrix for a given dimension, n, with a size of n x n. The unit matrix is also called the identity matrix. The MUNIT function takes just one argument, dimension, which should be a positive integer. The resulting matrix contains ones on the main diagonal and zeros in every other position.

### Examples

The formula in D5 returns a 3 x 3 unit matrix :

``````=MUNIT(3) // 3 x 3
``````

With 3 given for dimension, the MUNIT function returns a 3 by 3 array like this:

 1 0 0 0 1 0 0 0 1

The formula in J5 returns a 5 x 5 unit matrix.

``````=MUNIT(5) // 5 x 5
``````

With 5 given for dimension, the MUNIT function returns a 5 by 5 array like this:

 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1

### Array syntax

The MUNIT function returns an array of values. In Excel 365, where dynamic arrays are native, you can use the MUNIT function without any special handling – MUNIT will return an array of values that spill directly into cells in the worksheet.

In versions of Excel prior to Excel 365, you need to enter MUNIT enter as a multi-cell array formula to display results directly on the worksheet. To do this, make a selection of the right size, and enter MUNIT with control + shift + enter.

### Notes

• Dimension must be greater than zero.
• If dimension is zero or less than zero, MUNIT will return the #VALUE error.
• A unit matrix is also called an identity matrix. Author ### Dave Bruns

Hi - I'm Dave Bruns, and I run Exceljet with my wife, Lisa. Our goal is to help you work faster in Excel. We create short videos, and clear examples of formulas, functions, pivot tables, conditional formatting, and charts.