BY HAND$)**$ Given the matrix

$

A$=\backslash$begin$\{$bmatrix$\}$

$1$ & $0$ & $0\backslash \backslash 1$ &$2$ & $0\backslash \backslash 1$ & $2$ & $3$

$\backslash$end$\{$bmatrix$\}$

$$,$

use Gaussian $($Gauss$-$Jordan$)$ elimination to calculate its inverse. You must:

$($i$)$ explain the steps you followed, and

$($ii$)$ name the elementary matrices $($in the correct order$)$ used to reduce the matrix to the identity matrix. These are the elemanry matrices: E$1=$ np$.$array$([[1,0,0],$

$[-1,1,0],$

$[0,0,1]])$

E$2=$ np$.$array$([[1,0,0],$

$[0,1,0],$

$[-1,0,1]])$

E$3=$ np$.$array$([[1,0,0],$

$[0,1,0],$

$[0,-1,1]])$

E$4=$ np$.$array$([[1,0,0],$

$[0,1/2,0],$

$[0,0,1]])$

E$5=$ np$.$array$([[1,0,0],$

$[0,1,0],$

$[0,0,1/3]])$ show the whole detailed process please