Returns the matrix determinant of an array. Matrix determinants are generally used for solving systems of mathematical equations that involve several variables.
Syntax
MDETERM(array)
Argument 
Description 
Remarks 
array 
A numeric array with an equal number of rows and columns. 
 The array argument can be given as a cell range, such as A1:C3; as an array (array: A set of data used to build single formulas that produce multiple results or that operate on a group of arguments arranged in rows and columns. Excel has two kinds of arrays: array ranges and array constants. An array range is a rectangular area of cells that share a common formula; an array constant is a specially arranged group of constants that's used as an argument in a formula.), such as {1,2,3;4,5,6;7,8,9}; or as a name for either of these.
 If any cells in array are empty or contain text, this function returns the #VALUE! error value.
 This function returns the #VALUE! error value if array does not have an equal number of rows and columns.
 The matrix determinant is a number derived from the values in array. For a threerow, threecolumn array, A1:C3, the determinant is defined as:
=MDETERM(A1:C3) equals
A1*(B2*C3B3*C2) + A2*(B3*C1B1*C3) + A3*(B1*C2B2*C1)

General remarks
MDETERM is calculated with an accuracy of approximately 16 digits, which may lead to a small numeric error when the calculation is not complete. For example, the determinant of a singular matrix may differ from zero by 1E16.
Example
To make the following example easier to understand, you can copy the data to a blank sheet and then enter the function underneath the data. Do not select the row or column headings (1, 2, 3... A, B, C...) when you copy the sample data to a blank sheet.
Data 
Data 
Data 
Data 
1 
3 
8 
5 
1 
3 
6 
1 
1 
1 
1 
0 
7 
3 
10 
2 
Formula 
Description (Result) 


=MDETERM(A2:D5) 
Determinant of the matrix in the table (88) 


=MDETERM({3,6,1;1,1,0;3,10,2}) 
Determinant of the matrix as an array constant (1) 


=MDETERM({3,6;1,1}) 
Determinant of the matrix in the array constant (3) 


=MDETERM({1,3,8,5;1,3,6,1}) 
Returns an error because the array does not have an equal number of rows and columns (#VALUE!) 


See also
MINVERSE function
MMULT function
TRANSPOSE function
List of all functions (by category)