# MINVERSE function

Returns the inverse matrix for the matrix stored in an array.

## Syntax

MINVERSE(array)

Argument

Description

Remarks

array

A numeric array with an equal number of rows and columns.

• The array argument can be given as a cell range, such as A1:C3; as an array constantA set of data used to build single formulas that produce multiple results or that operate on a group of arguments arranged in rows and columns. Excel has two kinds of arrays: array ranges and array constants. An array range is a rectangular area of cells that share a common formula; an array constant is a specially arranged group of constants that's used as an argument in a formula., such as {1,2,3;4,5,6;7,8,9}; or as a name for either of these.

• If any cells in array are empty or contain text, this function returns the #VALUE! error value.

• This function returns the #VALUE! error value if array does not have an equal number of rows and columns.

## General remarks

• Formulas that return arrays must be entered as array formulas.

• Inverse matrices, like determinants, are generally used for solving systems of mathematical equations involving several variables. The product of a matrix and its inverse is the identity matrix — the square array in which the diagonal values equal 1, and all other values equal 0.

• As an example of how a two-row, two-column matrix is calculated, suppose that the range A1:B2 contains the letters a, b, c, and d that represent any four numbers. The following table shows the inverse of the matrix A1:B2.

 1 2
 A B d/(a*d-b*c) b/(b*c-a*d) c/(b*c-a*d) a/(a*d-b*c)
• MINVERSE is calculated with an accuracy of approximately 16 digits, which may lead to a small numeric error when the calculation is not complete.

• Some square matrices cannot be inverted and will return the #NUM! error value with MINVERSE. The determinant for a noninvertable matrix is 0.

 Tip  Use the INDEX (reference) function to access individual elements from the inverse matrix.

## Example 2: Returning Inverse matrix for the matrix stored in a three-column array

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