# Determinant (order n)

## Calculates the determinant of a square matrix of order n and the reciprocal of it.

 $\normal detA=det{A}={\left|\begin{array}\vspace{10} a_{\small 11}& a_{\small 12}& \cdots& a_{\small 1j}\\\vspace{10} a_{\small 21}& a_{\small 22}& \cdots& a_{\small 2j}\vspace{20}\\ \vdots& \vdots& \ddots& \vdots\vspace{10}\\a_{\small i1}& a_{\small i2}& \cdots& a_{\small ij}\\\end{array}\right|}\\$
 (enter a data after click each cell in matrix)
matrix A
{aij}

 det A
 1/ det A
 $\normal \\(1)\ detA={\large\sum_{\small j=1}^{\small n}}a_{\small ij}A_{\small ij},\hspace{20}A_{\small ij}:\ cofactor\\\vspace{10}(2)\ {\left|\begin{array}\vspace{10} a_{\small 11}& a_{\small 12}& a_{\small 13}\\\vspace{10} a_{\small 21}& a_{\small 22}& a_{\small 23}\\a_{\small 31}& a_{\small 32}& a_{\small 33}\\\end{array}\right|}\\\hspace{25}=a_{\small 11}{\left|\begin{array}\vspace{10} a_{\small 22}& a_{\small 23}\\ a_{\small 32}& a_{\small 33}\\\end{array}\right|}-a_{\small 12}{\left|\begin{array}\vspace{10} a_{\small 21}& a_{\small 23}\\ a_{\small 31}& a_{\small 33}\\\end{array}\right|}+a_{\small 13}{\left|\begin{array}\vspace{10} a_{\small 21}& a_{\small 22}\\ a_{\small 31}& a_{\small 32}\\\end{array}\right|}\\\vspace{10}(3)\ {\left|\begin{array}\vspace{10} a_{\small 11}& a_{\small 12}\\\vspace{10} a_{\small 21}& a_{\small 22}\\\end{array}\right|}=a_{\small 11}a_{\small 22}-a_{\small 21}a_{\small 12}\\$

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