The Excel MINVERSE function returns the inverse of a square matrix as a spilled array — the matrix that, multiplied by the original, gives the identity matrix. It is the backbone of solving systems of linear equations.
Syntax
| Argument | Description | |
|---|---|---|
array | Required | A square numeric range or array constant with a non-zero determinant. Commas separate columns and semicolons separate rows in an array constant. |
How to use it
MINVERSE returns an array the same size as the input, so in Excel 365 it spills across cells; in older Excel you select the output range and confirm with Ctrl+Shift+Enter.
For the matrix {4,7;2,6} the determinant is 4×6 − 7×2 = 10, so the inverse is 1/10 of {6,-7;-2,4}, giving {0.6,-0.7;-0.2,0.4}. Multiplying the matrix by its inverse with MMULT returns the identity matrix.
To solve A·x = b for x, compute =MMULT(MINVERSE(A), b).
Determinant must be non-zero. A singular matrix (determinant = 0) has no inverse, so MINVERSE returns #NUM!. Check first with MDETERM.
Try it: interactive demo
Pick a MINVERSE example to see the formula and its result.
Practice workbook
Frequently asked questions
How do I enter MINVERSE in older Excel?
Why does MINVERSE return #NUM!?
=MDETERM(array); a non-zero result means the inverse can be computed.What is the inverse of a matrix used for?
x = A⁻¹·b, computed as =MMULT(MINVERSE(A), b).How can I confirm the inverse is correct?
MMULT; the result should be the identity matrix (1s on the diagonal, 0s elsewhere), allowing for tiny floating-point dust.Master functions like this in one day
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