# MDETERM

Returns the matrix determinant of an array.

**Syntax**

**MDETERM**(**array**)

**Array** is a numeric array with an equal number of rows and columns.

- Array can be given as a cell range, for example, A1:C3; as an array constant, such as {1,2,3;4,5,6;7,8,9}; or as a name to either of these.
- If any cells in array are empty or contain text, MDETERM returns the #VALUE! error value.
- MDETERM also returns #VALUE! if array does not have an equal number of rows and columns.

**Remarks**

- The matrix determinant is a number derived from the values in array. For a three-row, three-column array, A1:C3, the determinant is defined as:
`MDETERM(A1:C3)`

equals`A1*(B2*C3-B3*C2) + A2*(B3*C1-B1*C3) + A3*(B1*C2-B2*C1)`

- Matrix determinants are generally used for solving systems of mathematical equations that involve several variables.
- 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 1E-16.

**Examples**

`MDETERM({1,3,8,5;1,3,6,1;1,1,1,0;7,3,10,2})`

equals 88

`MDETERM({3,6,1;1,1,0;3,10,2})`

equals 1

`MDETERM({3,6;1,1})`

equals -3

`MDETERM({1,3,8,5;1,3,6,1})`

equals #VALUE! because the array does not have an equal number of rows and columns.