In Python, use $\_\_$init$\_\_$ and $\_\_$str$\_\_$ to write a class Matrix for representing matrices over the real numbers R$.$ Then using that class do the following:

$1.$ Create a new method transpose$($self$)$ in the Matrix class which computes and returns a Matrix object representing the transpose of the matrix represented by self.

$2.$ Create a new method $\_\_$add$\_\_($self$,$ Op$2)$ which computes and returns a Matrix object representing the sum of the matrices represented by self and Op$2.$ If the sum is undefined then print an error and return None.

$3.$Create Matrix objects representing the matrices:

A$=([1\mathrm{.}1,2\mathrm{.}2,3\mathrm{.}3],[4\mathrm{.}4,5\mathrm{.}5,6\mathrm{.}6]),$B$=([3\mathrm{.}1,5\mathrm{.}1,2\mathrm{.}1],[1\mathrm{.}1,1\mathrm{.}2,1\mathrm{.}3])$

Test the methods above by using them to compute and print A$^($T$),$ B$^($T$),$ A$+$B$,$ A$^($T$)+$B$^($T$),$ and $($A$+$B$)^($T$).$

$4.$ Create a new method $\_\_$mul$\_\_($self$,$ Op$2)$ in the Matrix class which computes and returns a Matrix object representing the product of the matrices represented by self and Op$2.$ If the product is undefined, it should print an error and return None.

$5.$ Test the $\_\_$mul$\_\_$ method by using it to compute the matrix product AB$,$ where

A$=([3,1,1],[-1,2,1]),$ and B$=([1,2],[-1,2],[-1,-1])$