MINVERSE Function
Returns the inverse of a square matrix. It is mainly used when you need to solve matrix equations or verify matrix relationships.
Summary
MINVERSE returns the inverse of a square matrix. In practice, that matters when you are solving matrix equations or checking whether one matrix really reverses another.
The output is another matrix, not a single value. In current versions of Excel, the result spills automatically into the needed range. In older versions, Microsoft says you need to select the output range first and confirm the formula with Ctrl+Shift+Enter.
Purpose
Used when a square matrix needs to be inverted for further matrix calculations.
Return Value
The result has the same dimensions as the source matrix and spills into multiple cells in modern Excel.
Syntax
=MINVERSE(array)The input must be a square numeric matrix. Microsoft notes that MINVERSE returns #VALUE! if the array is not square or contains empty cells or text, and #NUM! if the matrix cannot be inverted.
Arguments
- array - Required. A square numeric range or array constant.
MINVERSE vs Other Matrix Functions
MINVERSE is not a starting point by itself. It usually sits in the middle of a matrix workflow, after you test the matrix and before you multiply the result with something else.
| Function | Main job | Returns | Use it when |
|---|---|---|---|
MINVERSE |
Inverts a matrix | An array | You need the inverse of a square matrix |
MDETERM |
Checks the determinant | One number | You want to see whether an inverse exists |
MMULT |
Multiplies matrices | An array | You want to test or use the inverse in another calculation |
MUNIT |
Builds an identity matrix | An array | You want a target shape to compare against after inversion |
Using MINVERSE
A good habit is to check the determinant first. If MDETERM returns 0, there is no inverse, so MINVERSE will return #NUM!. That quick check keeps the workbook easier to debug.
Another useful habit is verifying the result. Multiply the original matrix by its inverse with MMULT. If everything is correct, you should get an identity matrix, which is the same pattern that MUNIT creates. Because matrix math uses floating-point numbers, you may sometimes see tiny leftovers instead of clean zeros, so a light ROUND can help when you want the output to look cleaner.
Example 1 - Invert a 2x2 matrix
This is the easiest way to get used to the function. The source is 2x2, so the result also spills to 2x2.
=MINVERSE(B2:C3)Invert the 2x2 matrix in B2:C3. Formula: =MINVERSE(B2:C3).
Example 2 - Invert a 3x3 matrix
As long as the matrix is square and invertible, the same formula works on a larger range.
=MINVERSE(B2:D4)Calculate the inverse of the 3x3 matrix in B2:D4. Formula: =MINVERSE(B2:D4).
Example 3 - Watch for output space
In modern Excel, MINVERSE spills into nearby cells. If something blocks that spill range, you can run into a spill error instead of getting the full result.
=MINVERSE(B2:C3)Apply MINVERSE to B2:C3 and ensure results do not hit a #SPILL! error. Formula: =MINVERSE(B2:C3).
Example 4 - Check first, then invert
When you want a safer workflow, test the determinant before relying on the inverse.
=MDETERM(B2:C3)<>0Verify if B2:C3 has an inverse (Det <> 0). Formula: =MDETERM(B2:C3)<>0.
Conclusion Recap
- Main job:
MINVERSEreturns the inverse of a square matrix. - Shape rule: The input must be square and numeric.
- Common error:
#NUM!means the matrix has no inverse. - Good habit: Check
MDETERMfirst when the source matrix might be singular. - Best verification: Multiply the original matrix by the inverse and look for the identity matrix.
Tell your friends about this post