# Excel MINVERSE Function

The Excel MINVERSE function returns the inverse matrix of a given array. The input array must contain numbers only and be a square matrix, with equal rows and columns. The result is an inverse matrix with the same dimensions as the array provided.

*array*- A square array of numbers only.

The MINVERSE function returns the *inverse matrix* of a given array. The product of a matrix and its inverse is the *identity matrix*, a n × n square matrix with ones on the main diagonal and zeros in every other position.

The MINVERSE function takes just one argument, *array*, which should be a square matrix, with an equal number of rows and columns. In order for MINVERSE to calculate an inverse matrix, *array* must contain numbers only. When an inverse exists, MINVERSE returns an inverse matrix with the same dimensions as the *array* provided.

If a matrix cannot be inverted, MINVERSE will return a #NUM! error. A matrix that can't be inverted has a determinant of zero (0).

### Examples

In the example shown the formula used in E7 to calculate the inverse matrix of the 2 x 2 matrix in the range B7:C8 is:

=MINVERSE(B7:C8) // returns {-2,3;3,-4}

The result is the 2 x 2 matrix seen in E7:F8, which can also be expressed as the array {-2,3;3,-4}.

The formula in M7 calculates the inverse matrix of the 3 x 3 matrix in B7:C8:

=MINVERSE(I7:K9) // returns {-24,20,-5;18,-15,4;5,-4,1}

The result is the 3 x 3 matrix seen in M7:O9, which can be expressed as the array {-24,20,-5;18,-15,4;5,-4,1}.

### Array syntax

The MINVERSE function returns an array of values. In Excel 365, where dynamic arrays are native, you can use the MINVERSE function without any special handling – MINVERSE will return an array of values that spill directly into cells in the worksheet.

In versions of Excel *prior* to Excel 365, you need to enter MINVERSE enter as a multi-cell array formula to display results directly on the worksheet. To do this, make a selection of the right size, and enter MINVERSE with control + shift + enter.

### Notes

- The input array 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 in the source array will cause MINVERSE to return the #VALUE! error
- MINVERSE returns the #VALUE! error value if array does not have an equal number of rows and columns.
- If a matrix cannot be inverted, MINVERSE will return a #NUM! error.

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