MINVERSE: Matrix Inverses and Residual Checks in WPS Spreadsheet
Calculate a dense 2×2 inverse with MINVERSE and independently verify both identity products and a linear-system residual, with documented shape and entry limitations.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
MINVERSE returns the inverse matrix of a square numeric matrix when that inverse exists. It does not return the reciprocal of each cell and does not return the reciprocal determinant as its whole result. Its output has the same square shape as the input.
Syntax and historical entry workflow
=MINVERSE(array)
The official lesson requires a numeric array with equal row and column counts. It supports ranges and array constants, but the examples here use worksheet ranges to avoid unverified literal parsing. The lesson describes selecting the result area, editing with F2 and confirming Ctrl+Shift+Enter to display the array result. That is vendor documentation, not an array-entry test performed for this guide or proof of modern spilling.
Some introductory wording in the lesson loosely mixes matrices and determinants. The function’s defined result and worked array demonstration establish a matrix inverse; a determinant is instead a scalar.
Complete 2×2 input and inverse
Enter A2=2, B2=1, A3=1 and B3=3. For =MINVERSE(A2:B3), the independently expected result is:
0.6 -0.2
-0.2 0.4
For a matrix [a,b;c,d], the 2×2 determinant is ad−bc. Here it is 2×3−1×1=5. The inverse is (1/5) times [3,−1;−1,2], which gives the displayed mathematical array. The row separator in this explanation is mathematical notation, not a claim about WPS array-literal syntax.
Verify both multiplication orders
Multiply the original matrix A by the candidate inverse B independently:
- First row: 2×0.6+1×(−0.2)=1; 2×(−0.2)+1×0.4=0.
- Second row: 1×0.6+3×(−0.2)=0; 1×(−0.2)+3×0.4=1.
The reverse order BA also gives the 2×2 identity. Therefore the exact mathematical residual matrices AB−I and BA−I are zero. This is a genuine arithmetic inverse check, not a native recalculation result or a guarantee of zero floating-point residual in every implementation.
Additional dense controls
Each input below replaces A2:B3. Read the inner lists as rows.
| Input rows | Independently expected inverse rows |
|---|---|
| [1,2]; [3,4] | [−2,1]; [1.5,−0.5] |
| [3,1]; [2,1] | [1,−1]; [−2,3] |
| [1,−1]; [3,2] | [0.4,0.2]; [−0.6,0.2] |
The last control also agrees with the arithmetic of the vendor’s illustrated matrix. This does not turn the vendor capture into a native test by this task.
Practical linear-system check
For the primary A, consider right-hand side [5;7]. Multiplying the inverse by that column yields [1.6;1.8]. Substituting back gives 2×1.6+1.8=5 and 1.6+3×1.8=7. Both residuals are zero mathematically. This illustrates what the inverse means without claiming that explicit inversion is always the best numerical solution method.
Errors and limitations
The lesson documents #VALUE! for nonnumeric cells and nonsquare arrays. A singular matrix has no ordinary inverse mathematically; the cited lesson does not establish the exact singular-input error token, so none is invented here. A nearly singular matrix can amplify small perturbations even when an inverse exists.
All controls use small nonsingular dense matrices. No large-size capacity, precision, ill-conditioning guarantee, import behavior or current platform parity is inferred. A matrix result shown as only one cell is not enough evidence that all inverse components were obtained; check the documented output shape separately from the mathematical values.
Availability and evidence
The official WPS lesson is dated 2019-05-29 and explicitly labels its applicability WPS Office for Windows Personal. It does not identify a numeric release. This establishes documentation by that date, not the function’s original introduction or its last working version. Current build limits and equivalence across WPS clients remain unverified. The available evidence does not establish retirement or formal deprecation.
Checked October 18, 2026. The examples in this guide are original, independently calculated controls based on the lesson. They have not been run in WPS or another spreadsheet application. No screenshot or execution result is claimed.