## Purpose

## Return value

## 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.