I would appreciate it if you could explain each part in detail step by step and show me the final version that was integrated at the end.

e$.$ Show the value of the state matrix after MixRows $($Only the value for $Y)$

Example: for $x$

We must compute$\backslash$end$\{$array$\}\backslash$right$]=\backslash$left$[\{$:$[02,03,01,01],[$ddots$,*,$ddots,$*],[.,.,$ddots,$*]$:$\}\backslash$right$]\backslash$times$\backslash$left$[\{$:$[7$C$],[$F$2],[2$B$],[$AB$]$:$\}\backslash$right$]]$

We have:

$[02].[7$C$]=[02]*[01111100]=$

$[03]*[F2]=[02]*[11110010]o+[01][11110010]$

$=([11100100]o+[00011011])o+[11110010]=$

$[01]*[2B]=[00101011]=$

$[01]*[AB]=[10101011]=$

The XOR sum is:

$[00001101]$

$[00101011]$

$x=\left[\begin{array}{ccccccc}0& 1& 1& 1& 0& 1& 0\end{array}\right]=[75]$

Now compute Y$.$