Zoho Sheet MUNIT: Identity Matrices, Sizes and Multiplication Checks
Build identity matrices in Zoho Sheet, verify every output cell and choose the correct identity size for square or rectangular matrix multiplication.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
MUNIT creates an identity matrix: ones on the main diagonal and zeros everywhere else. Multiplying a compatible matrix by an identity preserves it. This makes the function a useful control when learning matrix formulas or checking an inverse.
An identity matrix is different from a matrix filled with ones. The off-diagonal zeros are what prevent unrelated rows or columns from being added together.
Availability and version history
- Introduced: The first introduction release and date are not established by the checked references.
- Availability: Listed in the current Zoho Sheet function help; no final supported-version endpoint is established.
- Scope: Current web-service documentation. Historical builds, mobile clients, offline use and imported workbooks remain separately unverified.
- Checked: October 14, 2026, against the official MUNIT reference. All worked outputs were independently calculated; no native Zoho Sheet test was performed.
Syntax and size
MUNIT(size)
The MUNIT reference defines size as a positive integer. A size of 3 means three rows and three columns, not three total cells. The argument has no documented default.
The same entry explicitly lists #VALUE! for a size less than or equal to zero. Thus zero and -1 are documentation-backed error examples, not additional native observations. Fractional-size conversion, extreme dimensions and text coercion are not established here.
Zoho’s dynamic-array instructions describe entering an array formula in one cell with ordinary Enter. Leave its output rectangle empty; an obstruction produces #SPILL!. Enter only the anchor formula, rather than filling copies across the output. These exercises follow that documented web workflow.
Generate and inspect a three-by-three identity
Create IdentityCheck, reserving A1:O12. Leave A2:C4 empty and put =MUNIT(3) in A2. Expect:
| Output row | A | B | C |
|---|---|---|---|
| 2 | 1 | 0 | 0 |
| 3 | 0 | 1 | 0 |
| 4 | 0 | 0 | 1 |
This is the three-by-three pattern printed in the official example. In A7 enter =A2+B3+C4 for a diagonal sum of 3. In A8 enter =MDETERM(A2:C4) for 1.
The diagonal sum counts three ones; the determinant is a different calculation. It is not three merely because the matrix has three rows. MDETERM supplies the determinant control.
For the other official example, create IdentityTwo, leave A2:B3 empty and enter =MUNIT(2) in A2. The rows are 1,0 and 0,1. On a separate IdentityOne sheet, =MUNIT(1) in A2 has the independently expected single value 1.
Multiply on either side of a square matrix
Return to IdentityCheck. Put these values in E2:G4, leaving I2:K4 and M2:O4 empty:
| Row | E | F | G |
|---|---|---|---|
| 2 | 2 | -1 | 4 |
| 3 | 0 | 3 | 5 |
| 4 | 7 | 2 | 1 |
In I2 enter =MMULT(A2:C4;E2:G4). In M2 enter =MMULT(E2:G4;A2:C4). Both output grids have the exact expected rows 2,-1,4, 0,3,5, 7,2,1.
For a complete comparison, put =I2-E2 in I7, fill across through K7, then fill I7:K7 down through row 9. Put =M2-E2 in M7, fill through O7 and then down through row 9. All eighteen differences have expected value 0.
The relative references track the matching source entries. These are ordinary scalar subtraction checks outside the array output areas; they do not overwrite the identity or either product.
Advanced: rectangular matrices need different identity sizes
Create RectangularIdentity, reserving A1:P8. Enter rows 2,1, 1,3, 4,2 in A2:B4.
- Leave D2:F4 empty; enter
=MUNIT(3)in D2. - Leave H2:I3 empty; enter
=MUNIT(2)in H2. - Leave K2:L4 empty; enter
=MMULT(D2:F4;A2:B4)in K2. - Leave N2:O4 empty; enter
=MMULT(A2:B4;H2:I3)in N2.
Both final products reproduce 2,1, 1,3, 4,2. The left identity is 3×3 because it combines with the three rows of the input; the right identity is 2×2 because it combines with its two columns.
The corresponding shape checks are 3×3 times 3×2, and 3×2 times 2×2. Using the two-by-two identity on the left instead would violate the MMULT shared-dimension requirement. An identity is neutral only when its size fits its position.
Why a matrix of ones is different
On a new AllOnes sheet, enter ones in all four cells A2:B3 and enter rows 2,4 and 6,8 in D2:E3. Leave G2:H3 empty and put =MMULT(A2:B3;D2:E3) in G2.
The mathematical result has rows 8,12 and 8,12, not the original rows. Each output row adds both source rows because the left matrix contains two ones per row. An identity instead selects one source row at a time.
This comparison helps catch a common setup mistake: entering ones throughout a rectangle does not create a unit matrix. Verify both the diagonal and the off-diagonal positions before using it as a control.
Practical boundaries
Keep labels above or beside spill rectangles rather than inside them. If the intended output overlaps unrelated data, use another location; an obstructed result should not be repaired by overwriting source cells.
An identity control checks a multiplication operation on the stated inputs, but does not establish that an imported workbook preserves formulas or that every platform implements the same numeric limits. MINVERSE returns a matrix inverse; it does not generate an identity directly.
The examples contain ordinary numeric cells and use semicolons between multiple arguments, matching the English function references. Check the formula separators in your workbook. Source blanks, numeric text, Boolean values, existing error cells and imported array formulas are outside the tested mathematical fixtures.