# Manuals/calci/DET

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**DET(array)**

- is the set of numbers.

## Description

- This function gives the determinant value of a matrix.
- To calculate the determinant of a matrix, we can choose only square matrix.i.e. Number of rows and number of columns should be equal.
- Determinant of the identity matrix is always 1.
- Determinant of the matrix is denoted by or .
- Let be 2x2 matrix with the elements

- Then , where all are real numbers.
- Let be the 3x3 matrix with the elements

Then :

- Let be a square matrix of order . Write ,
- Where is the entry on the row and column and to & to .
- For any and , set (called the co-factors), then the general formula for determinant of the matrix is,

, for any fixed . Also, for any fixed .

- This function will give the result as error when

1. Any one of the element in array is empty or contain non-numeric 2. Number of rows is not equal to number of columns

## Examples

- =DET([[6,4,8],[3,6,1],[2,4,5]]) = 104
- =DET([[-5,10],[6,-8]]) = -20
- =DET([[1,0,2,1],[4,0,2,-1],[1,4,5,2],[3,1,2,0]]) = 17
- =DET([1,2,3],[5,2,8]) = NAN

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