The MINVERSE function returns the inverse matrix for the matrix stored in an array.

### Syntax

=MINVERSE(array)

#### Arguments

Argument Description
array A numeric array with an equal number of rows and columns. array can be given as:

 • a range of cells, such as A1:C3 • an array constant, such as {1,2,3;4,5,6;7,8,9} • a name for either of the above

Inputting  Array Formulas: To input an array formula,

1. highlight the range of cells for the function result,
2. type the function into the first cell of the range, and
3. press CTRL-SHIFT-ENTER

#### Examples

A B C D E F G H I
1 Data Data Data   Formula Results Notes
2 1 0 1   {=MINVERSE(A2:C4)} 2.5 -1 0.5 To work correctly, the formula needs to be entered as an array formula by pressing Ctrl+Shift+Enter
3 2 1 4     1 -1 1
4 1 2 3     -1.5 1 -0.5
5
6 Data Data Data
7 1 2 1   {=MINVERSE(A7:C9)} 0.25 0.25 -0.75
8 3 4 -1     0 0 0.5
9 0 2 0     0.75 -0.25 -0.25

Note: The curly brackets, { and }, seen in the formulas in E2 and E7 are not entered by the user. Excel applies these to show the formula has been input as an array formula.

#### Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if either:

 • the supplied array contains a blank or a non-numeric value • the supplied array does not have equal numbers of rows and columns
#NUM! Occurs if the supplied matrix is singular, i.e. there is no inverse for the supplied matrix
#N/A Occurs in cells outside the range of the resulting matrix, e.g. in the example above, had we highlighted cells F7-H10 before entering the MINVERSE function, cells, F10-H10 are not part of the resulting matrix and therefore will return the #N/A error

The inverse of a square matrix is the matrix with the same dimensions that, when multiplied with the original matrix, gives the Identity matrix:

If an inverse exists, the original matrix is know as invertible. Otherwise, the original matrix is described as singular.

See Wikipedia for more information on matrix inversion.