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:    

    \[     \left[  \begin{array}{ccccc} 1 & 0 & 0 & \cdots & 0  \\ 0 & 1 & 0 & \cdots & 0  \\ 0 & 0 & 1 & \cdots & 0  \\ \vdots & \vdots & \vdots & \ddots & \vdots  \\ 0 & 0 & 0 & \cdots & 1  \end{array} \right]    \]

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.