Exercise $28$ Equivalence of regular languages

$(6$ points$)$

Let the following deterministic finite automata $M_1$ and $M_2$ over the alphabet $=\{a,b\}$ be given:

Check whether both deterministic finite automata are equivalent. Two finite automata are equivalent, if the following holds:

$T(M_1)=T(M_2)$

First of all construct the minimal automata of $M_1$ and $M_2$ by means of the algorithm presented in the lecture $(4$ points$)$ and argue with the aid of the minimal automata, why $M_1$ and $M_2$ are $($not$)$ equivalent $(2$ points$).$

Indicate all intermediate steps of the algorithm $($i$.$e$.$ what you marked and why$).$ Submissions without intermediate steps do not achieve points!

$($Note: Minimal automata for a language are unique up to the naming of states.$)$

$($In total, there are $20$ points in this exercise sheet.$)$