# Manuals/calci/MATRIXDETERMINANT

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**MATRIXDETERMINANT (a)**

- is any square matrix.

## Description

- This function is calculating the determinant of the given matrix.
- In , is any square matrix.
- The determinant of a matrix is a special number that can be calculated from a square matrix.
- The determinant of a 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 .

## Examples

- MATRIXDETERMINANT([[6,4,8],[3,6,1],[2,4,5]]) = 104.00000000000001
- MATRIXDETERMINANT([[8,-4],[12,5]]) =88
- MATRIXDETERMINANT([1,2,3,4;5,6,-7,8;12,10,-13,15;11,7,5,3]) = 1514