MINVERSE in Excel: Invert a Numeric Matrix and Verify the Product
Build an Excel inverse matrix from a complete dataset, verify identity products, solve a small system and distinguish input errors from singularity.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: MINVERSE returns the inverse of a square numeric matrix when an inverse exists. For rows 2,1 and 1,3, the expected inverse has rows 0.6,-0.2 and -0.2,0.4. Multiply the result by the original matrix to check it.
Availability and version history
- Introduced: first introduction version is not established by the official history reviewed; the current product list is not a launch record.
- Availability: official help lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
- Checked: October 14, 2026; official MINVERSE reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.
Syntax and array-entry scope
=MINVERSE(array)
The input must be square and contain only numbers. Microsoft documents #VALUE! for non-square inputs or blank/text cells, and #NUM! for a matrix that cannot be inverted.
Microsoft describes top-left-cell entry followed by Enter for current Microsoft 365 dynamic arrays. In older non-dynamic-array builds, select the full output area and use the documented legacy array-entry workflow, including Ctrl+Shift+Enter where that is the supported command. Confirm the workflow in the actual client; a shared product list does not certify every keyboard shortcut or spill behavior.
Example 1: invert a two-by-two matrix
Enter A2:B3:
| A | B |
|---|---|
| 2 | 1 |
| 1 | 3 |
Put =MINVERSE(A2:B3) in a clear two-by-two output area using the appropriate array workflow. The explanatory headings below label columns, not an extra generated row:
| First output column | Second output column |
|---|---|
| 0.6 | -0.2 |
| -0.2 | 0.4 |
The determinant is 5. The independent two-by-two inverse is one fifth of rows 3,-1 and -1,2. This produces the displayed matrix without relying on a captured Excel calculation.
Example 2: multiply back to the identity
=MMULT(A2:B3,MINVERSE(A2:B3))
=MMULT(MINVERSE(A2:B3),A2:B3)
Both expected outputs are the two-by-two identity: rows 1,0 and 0,1. For example, the upper-left entry is 2×0.6+1×(-0.2)=1, and the upper-right is 2×(-0.2)+1×0.4=0.
Use full calculated values rather than typing shortened decimals from a larger inverse. MMULT computes matrix multiplication, not cell-by-cell multiplication.
Advanced example: solve a small linear system
Suppose the equations are 2x+y=5 and x+3y=7. Keep their coefficient matrix in A2:B3 and enter 5,7 in D2:D3:
=MMULT(MINVERSE(A2:B3),D2:D3)
Expected two-row result: x=1.6 and y=1.8. Substitute those values into the original equations: 2×1.6+1.8=5 and 1.6+3×1.8=7.
The substitution is an independent residual check. It is essential that the coefficient columns and output-variable order agree; swapping x and y in only one place solves a different system.
Advanced example: scale the matrix and inspect the inverse
Enter F2:G3 as rows 4,2 and 2,6, twice the original matrix:
=MINVERSE(F2:G3)
Expected inverse rows are 0.3,-0.1 and -0.1,0.2, half of the original inverse. Multiplying 2A by half of A’s inverse still gives the identity.
The inverse of a scaled matrix is not obtained by scaling its inverse in the same direction. This finite control helps expose a copied coefficient-scale error.
Advanced check: distinguish singularity from an input-type error
Enter H2:I3 as rows 2,1 and 4,2. The second row is twice the first, so the determinant is mathematically zero and no ordinary inverse exists. =MINVERSE(H2:I3) has Microsoft’s documented expected error #NUM! for a noninvertible matrix.
Replacing one entry with a text label or leaving a cell empty instead violates the numeric-input requirement, for which Microsoft documents #VALUE!. A numeric zero is allowed in a matrix and is not the same as an empty cell.
Numerical precision and troubleshooting
Microsoft describes approximately 16-digit calculation accuracy and cautions that cancellation can leave small errors. A computed product may therefore be close to the identity rather than exactly equal in every displayed bit.
A nonzero MDETERM result is not by itself a guarantee of a well-conditioned numerical inverse. Small perturbations can matter for nearly dependent rows. Check residuals in the scale of the actual model instead of adopting an arbitrary universal tolerance.
No maximum-size benchmark, native error screenshot, universal spill behavior or cross-platform numerical certification is claimed. Keep the complete numeric dataset and output dimensions visible when reproducing these controls.
References and verification
Inputs are fictional. Decimal answers are independent mathematical expectations rounded to nine places, not captured native results. Extreme magnitudes, complete coercion matrices and cross-version numerical accuracy remain untested.