## Purpose

## Return value

## Syntax

`=MDETERM(array)`

*array*- A square array of numbers only.

## How to use

The MDETERM function returns the matrix determinant of a given *array*, which must be a square matrix containing numbers only, and no empty values. In mathematics, the matrix determinant is a scalar value (single value) that is a function of the entries in a square matrix. The determinant is a special number that can help characterize some properties of the matrix. For example, if the determinant is zero, the matrix will not have an inverse.

The MDETERM function takes just one argument, *array*, which can be provided as a range or an array constant. *Array* must be a square matrix with the same numbers of rows and columns.

### Examples

To get the matrix determinant for the 2 x 2 array shown in B7:C8, the formula in E7 is:

```
=MDETERM(B7:C8) // returns -1
```

The equivalent formula with an array constant is:

```
=MDETERM({4,3;3,2}) // returns -1
```

To get the matrix determinant for the 3 x 3 array shown in I7:K9, the formula in M7 is:

```
=MDETERM(I7:K9) // returns 1
```

The equivalent formula with an array constant is:

```
=MDETERM({1,0,5;2,1,6;3,4,0}) // returns 1
```

### Notes

- The
*array*argument must be a square matrix with an equal number of rows and columns - The
*array*argument can be provided as a range or array constant like {4,3;3,2} - Empty cells or text in
*array*will cause MDETERM to return a #VALUE! error - MDETERM returns a #VALUE! if
*array*does not have an equal number of rows and columns