## How to use the MUNIT function

**What is the MUNIT function?**

The MUNITÂ function calculatesÂ the identity matrix for a given dimension.

**What is an identity matrix?**

An identity matrix is a square matrix with 1s on the main diagonal and 0s elsewhere. It is often denoted by the capital letter I.

For example, a 2x2 identity matrix:

I = [[1, 0],

[0, 1]]

Identity matrices are fundamental to linear algebra and matrix operations.

**What applications does the identity matrix have?**

- Multiplying by the identity matrix leaves the original matrix unchanged.
- Finding the inverse of a matrix involves multiplying by the identity matrix.

**Explain how multiplying by the identity matrix returns the original matrix?**

Let's say we have the matrix:

A = [[1, 2], [3, 4]]

And the 2x2 identity matrix:

I = [[1, 0], [0, 1]]

When we multiply A and I:

A x I = [[1, 2], x [[1, 0], [3, 4]] [0, 1]]

= [[1, 2], [3, 4]]

**What is the inverse of a matrix?**

For a matrix A, its inverse matrix is denoted A-1. For A to have an inverse it must be a square matrix and have non-zero determinants.

Matrix inversion is a fundamental linear algebra operation. The inverse matrix has applications in solving matrix equations, finding bases, and transforming coordinates.

How to calculate the inverse of a 2x2 matrix:

A = [[a, b], [c, d]]

To find the inverse A-1:

- Calculate the determinant of A: det(A) = ad - bc
- Find the adjoint of A: adj(A) = [[d, -b], [-c, a]]
- Compute the inverse: A-1 = 1/det(A) * adj(A)

**What is an adjoint?**

The adjoint of a matrix, also called the adjugate matrix, and is useful for finding the inverse of a square matrix.

To get the adjoint of an n x n matrix A:

- Calculate the matrix of cofactors of A, denoted C.
- Take the transpose of C to obtain the adjoint matrix, denoted adj(A).

The cofactor matrix C is obtained by replacing each element of A with its cofactor, which involves cross products of matrix minors.

**What is a determinant?**

The determinant is a special scalar value computed from a square matrix that provides crucial information about matrix properties and transformations.

Denoted as det(A) or |A| for a matrix A.

Given the matrix:

A = [[a, b], [c, d]]

The determinant is calculated as:

det(A) = ad - bc

For example:

B = [[3, 2], [1, 4]]

det(B) = (3)(4) - (2)(1) = 12 - 2 = 10

**What are the matrix functions in Excel?**

Function | Description |
---|---|

MMULT(array1, array2) | Returns the matrix product of two arrays. |

MUNIT(dimension) | Returns the matrix identity for the specified dimension. |

MINVERSE(array) | Returns the matrix inverse of the given array. |

### Excel Function Syntax

MUNIT(*dimension*)

### Arguments

dimension |
Required. An integer that determines the dimension of the returning unit matrix. |

### MUNIT function example

Array formula in cell B2:

The formula above returns an identity matrix with dimensionÂ 3, meaning the matrix is 3x3 and has ones on the main diagonal and zeros elsewhere.

The MUNIT function returns an array, you need to enter the function as an array formula.

*To enter an array formula, type the formula in a cell then press and hold CTRL + SHIFT simultaneously, now press Enter once. Release all keys.*

*The formula bar now shows the formula with aÂ beginning and ending curly bracket telling you that you entered the formula successfully. Don't enter the curly brackets yourself.*

The dimension argument must be larger than 0 (zero).

### MUNIT function not working

The MUNTI function returns #VALUE if the dimension argument is smaller than or equal to 0 (zero).

### Functions in 'Math and trigonometry' category

The MUNIT function function is one of many functions in the 'Math and trigonometry' category.

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