# 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.

### 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.
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.

To make the following example easier to understand, you can copy the data to a blank sheet and then enter the function underneath the data. Do not select the row or column headings (1, 2, 3... A, B, C...) when you copy the sample data to a blank sheet.

Note   The formula in the example must be entered as an array formula. First, type the formula into cell A5 and then press RETURN . The single result is 0. Next, select the range A5:B6, press CONTROL + U , and then press + RETURN . The array results, from left to right and top to bottom, are 0, 0.5, -1, and 2.

Data Data
4 -1
2 0
Formula
=MINVERSE(A2:B3)

To make the following example easier to understand, you can copy the data to a blank sheet and then enter the function underneath the data. Do not select the row or column headings (1, 2, 3... A, B, C...) when you copy the sample data to a blank sheet.

Note   The formula in the example must be entered as an array formula. First, type the formula into cell A6 and then press RETURN . The single result is 0.25. Next, select the range A6:C8, press CONTROL + U , and then press + RETURN . The array results, from left to right and top to bottom, are 0.25, 0.25, -0.75, 0, 0, 0.5, 0.75, -0.25, and -0.25.

Data Data Data
1 2 1
3 4 -1
0 2 0
Formula
=MINVERSE(A2:C4)

INDEX (array) function

INDEX (reference) function

MMULT function

TRANSPOSE function

List of all functions (by category)

Applies to:
Excel for Mac 2011