Summary

The Excel MDETERM function returns the determinant of a square matrix. A determinant is a single number derived from the values in that matrix, and one of its most important uses in Excel is checking whether a matrix can be inverted.

If the determinant is 0, the matrix is singular and MINVERSE cannot return an inverse. If the determinant is not 0, the matrix is invertible in the usual matrix sense. That is why MDETERM is often used as a diagnostic step before other matrix calculations.

Syntax

=MDETERM(array)

The argument must be a square numeric array. Microsoft also notes that the array can be provided as a cell range, an array constant, or a named range.

Arguments

• array - [required] A numeric array with an equal number of rows and columns.

MDETERM and Matrix Status

Microsoft notes that MDETERM is calculated with about 16 digits of accuracy, so a singular matrix may sometimes return a very small value such as 1E-16 instead of an exact 0 because of floating-point arithmetic.

Using MDETERM

The most common use of MDETERM in Excel is as a check before matrix inversion. If you plan to use MINVERSE, testing the determinant first can tell you whether the matrix is invertible. This is a practical way to avoid running into a #NUM! result later in the process.

MDETERM is also useful because it condenses the matrix into one scalar result. That makes it a convenient summary value when you need to judge whether the rows or columns are linearly dependent, or whether a transformation matrix collapses area rather than preserving it.

For 2x2 matrices, the determinant is still easy to compute by hand as ad-bc. For larger matrices, Excel becomes much more helpful because the manual calculation grows quickly in length and is easy to get wrong.

Example 1 - Calculate a 2x2 Determinant

This is the most direct use of the function.

=MDETERM(A1:B2)

If A1:B2 contains [[4,7],[2,6]], the determinant is 10. This matches the familiar 2x2 rule (4x6)-(7x2).

Example 2 - Check Invertibility

A determinant of 0 means the matrix cannot be inverted.

=MDETERM(A1:B2)

If the second row is just a multiple of the first, the determinant becomes 0. That is the clearest sign that the matrix is singular and that MINVERSE will fail.

Example 3 - Work with a 3x3 Matrix

This is where Excel saves you time.

=MDETERM(A1:C3)

The result is still a single number, even though the input is a 3x3 matrix. That makes MDETERM useful as a compact diagnostic step before more complex matrix operations.

Example 4 - Interpret a Scaling Matrix

For a 2x2 transformation matrix, the determinant can be read as an area scaling factor.

=MDETERM(A1:B2)

If the matrix doubles one axis and doubles the other, the determinant becomes 4. That indicates the transformed area is four times the original area.

MDETERM returns #VALUE! when the array is not square or when any cell in the array is empty or contains text. That makes input quality part of the calculation, not just a formatting issue.

• MDETERM always returns one number, regardless of matrix size.
• The matrix must be square and numeric.
• A zero determinant is the main warning sign that no inverse exists.

Conclusion Recap

• Summary: MDETERM returns the determinant of a square matrix.
• Key use: Check whether a matrix is invertible before using MINVERSE.
• Main rule: The input must be square and fully numeric.
• Error behavior: #VALUE! appears for non-square or nonnumeric input.
• Important signal: A determinant of 0 means the matrix is singular.