MDETERM: Scalar Matrix Determinants in WPS Spreadsheet
Calculate dense 2×2 determinants with MDETERM, including sign reversal, singular zero and inverse consistency, while distinguishing scalar output and documented errors.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
MDETERM returns the determinant, a single scalar associated with a square numeric matrix. It does not return an inverse matrix or multiply the matrix’s entries indiscriminately. For a 2×2 matrix, the determinant is the product of the main diagonal minus the product of the other diagonal.
Syntax and scalar output
=MDETERM(array)
The official lesson requires equal row and column counts and numeric entries. It permits ranges or array constants; this guide uses dense numeric worksheet ranges. Unlike an inverse or matrix product, a determinant has one scalar result. The fact that a vendor walkthrough selected more than one worksheet cell does not change that mathematical output type.
Step-by-step determinant
Enter A2=2, B2=1, A3=1 and B3=3. Then use =MDETERM(A2:B3). The calculation is:
(2 × 3) − (1 × 1) = 5
The expected answer is 5. It is not 2×1×1×3=6. The subtraction and position of the entries matter.
Original dense numeric controls
Replace A2:B3 for each example and use the same formula. Each pair of bracketed lists describes the top and bottom row, rather than literal parser syntax.
| Matrix rows | ad−bc | Expected determinant |
|---|---|---|
| [2,1]; [1,3] | 6−1 | 5 |
| [1,2]; [3,4] | 4−6 | −2 |
| [1,−1]; [3,2] | 2−(−3) | 5 |
| [3,4]; [1,2] | 6−4 | 2 |
| [2,4]; [1,2] | 4−4 | 0 |
The fourth row swaps the rows of the second matrix, changing the determinant’s sign. The last matrix has one row twice the other, giving zero. A zero determinant is a valid mathematical scalar; it is not an error merely because the matrix would be singular for inversion.
Practical interpretation and a consistency check
For a square matrix, a nonzero determinant establishes invertibility in exact mathematics. The primary matrix’s determinant 5 supports the inverse [0.6,−0.2;−0.2,0.4]. That inverse has determinant 0.6×0.4−(−0.2)×(−0.2)=0.2, the reciprocal of 5. This is an independent algebraic check, not a WPS execution.
A determinant is also signed: negative does not mean an arithmetic failure. In a two-dimensional linear transformation, its magnitude describes area scaling and its sign distinguishes orientation. Those interpretations depend on the surrounding mathematical model, not on worksheet formatting.
Why a tiny determinant needs caution
Although zero versus nonzero is decisive in exact algebra, a floating-point number displayed near zero is not a complete numerical conditioning assessment. Matrix scaling can change determinant magnitude without making that magnitude alone a reliable indicator of solver accuracy. The small exact controls do not establish tolerances for large or ill-conditioned matrices.
Documented errors and scope
The lesson specifies #VALUE! if entries are nonnumeric or the array is not square. Those are source-attributed expectations; no native error behavior was observed here. A numeric zero entry is allowed in a numeric matrix and differs from a blank or text cell.
The source does not establish a current maximum matrix size, numerical precision guarantee or array-constant locale behavior. Keep the input shape explicit and inspect values before relying on a determinant. Use an inverse or matrix-product function when the desired output is a matrix rather than this scalar.
Availability and evidence
The official WPS lesson is dated 2019-06-10 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.