# Manuals/calci/MATRIXDETERMINANT

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

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

Determinants