$4\mathrm{.}24$ Write a user$-$defined MATLAB function that determines the inverse of a matrix using the Gauss$-$Jor$-$

dan 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 $\left[\begin{array}{ccc}-1& 2& 1\\ 2& 2& -4\\ 0\mathrm{.}2& 1& 0\mathrm{.}5\end{array}\right].$

$($b$)$ The matrix $\left[\begin{array}{cccc}-1& -2& 1& 2\\ 1& 1& -4& -2\\ 1& -2& -4& -2\\ 2& -4& 1& -2\end{array}\right].$

Hint: in your code, construct a matrix, $AB=[AB],$ where $A$ is the input square matrix and $B$ is the identity matrix. In order to perform Gauss$-$Jordan

on $AB,$ you need to use row operations on $AB$ such that the columns corresponding to A become the identity matrix, and the columns holding $B$

will be the inverse.

Note: No need of pivoting for this code.

$[]$ import numpy as np

def Inverse$($A$)$:

return

$[]$ #Output

#Answer for a$)$

#Answer for b$)$