Write a working Python$/$R function that determines the inverse of a matrix using the Gauss$-$Jordan method. For the function name and arguments use Ainv $=$ Inverse $($A$),$ where A is the matrix to be

inverted, and Ainv is the inverse of the matrix. Use the Inverse function to calculate the inverse of:

$($a$)$ The matrix $\left[\begin{array}{ccc}-1& 2& 1\\ 2& 2& -4\\ 0\mathrm{.}2& 1& 0\mathrm{.}5\end{array}\right]$

Requirements:

$-$This function must be able to handle pivoting.

$-$ The built$-$in inverse function in Numpy$/$Scipy must NOT be used in the user defined

function.