Summary

The Excel MINVERSE function returns the inverse of a square matrix stored in an array. If matrix A has an inverse, then multiplying A by MINVERSE(A) gives the identity matrix, which has 1s on the main diagonal and 0s elsewhere.

In practice, MINVERSE is mainly used with other matrix functions such as MMULT and MDETERM. A common pattern is using it to solve a system of linear equations or to verify that a matrix operation can be reversed correctly.

Syntax

=MINVERSE(array)

The array argument must be a square numeric array, meaning it needs the same number of rows and columns. Microsoft also notes that if you are using Microsoft 365, you can enter the formula in the top-left output cell and let the result spill. In older Excel versions, you must select the whole output range first and confirm the formula as an array formula with Ctrl+Shift+Enter.

Arguments

• array - [required] A square numeric array or range with equal rows and columns.

MINVERSE vs Related Matrix Functions

Using MINVERSE

The first thing to remember is that MINVERSE only works on square numeric matrices. If the range contains text, empty cells, or has a different number of rows and columns, Excel returns #VALUE!. If the matrix is square but cannot be inverted, Excel returns #NUM!. Microsoft notes that a noninvertible matrix has a determinant of 0, so MDETERM is a useful check before you attempt the inversion.

MINVERSE is usually not the last step by itself. Most of the time, it is part of a larger workflow. You might invert a matrix and then multiply it by another matrix or by a result vector with MMULT. That is why MINVERSE appears so often in lessons together with other matrix functions rather than as a standalone calculation.

It is also worth remembering that matrix results are numeric approximations. Microsoft notes that MINVERSE is calculated with about 16 digits of accuracy, so small rounding differences can appear in some results. For example, when you multiply a matrix by its inverse, values that should be 0 may appear as tiny decimals because of normal floating-point behavior.

Example 1 - Invert a 2x2 Matrix

This is the basic use of the function.

=MINVERSE(A1:B2)

If A1:B2 contains a valid 2x2 matrix, MINVERSE returns another 2x2 array. The returned values are the inverse of the original matrix, not just a single number, so the output needs enough empty space to spill into.

Example 2 - Verify the Identity Property

A good way to check your result is to multiply the matrix by its inverse.

=MMULT(A1:B2,MINVERSE(A1:B2))

The result should be the identity matrix, which for a 2x2 case looks like [[1,0],[0,1]]. This does not just prove the formula worked; it also helps you understand what an inverse matrix is supposed to do.

Example 3 - Solve x from Ax=b

This is one of the most practical reasons to use MINVERSE.

=MMULT(MINVERSE(A1:B2),E1:E2)

Here, A1:B2 is matrix A and E1:E2 is vector b. The formula returns the solution vector x. This is a common teaching example because it shows how MINVERSE fits into a larger matrix calculation instead of being used on its own.

Example 4 - Try a Singular Matrix

Not every square matrix has an inverse.

=MINVERSE(A3:B4)

If A3:B4 contains a singular matrix, Excel returns #NUM!. In the sample matrix, the second row is just a multiple of the first row, so the matrix cannot be reversed. This is why checking the determinant with MDETERM is often a good habit.

One practical note for modern Excel: because MINVERSE returns multiple cells, the spill range has to be clear. If other values block the output area, Excel may return a spill error instead of the matrix result. Clearing enough room before entering the formula usually solves that problem.

• MINVERSE only works on square matrices.
• Text or empty cells inside the matrix cause #VALUE!.
• A singular matrix returns #NUM!.
• Use MMULT to verify the inverse or solve a matrix equation.

Conclusion Recap

• Summary: MINVERSE returns the inverse of a square numeric matrix.
• Key rule: The input must be square and invertible.
• Error behavior: Non-square or nonnumeric input gives #VALUE!, while a singular matrix gives #NUM!.
• Common pattern: Use MMULT(A,MINVERSE(A)) to verify the identity result.
• Practical use: Use MMULT(MINVERSE(A),b) to solve a small linear system.