Apply formula based on the equality of adjacent cells

Hey guys,
I hope you are well.
There is a task where somebody will enter values in column A.
The values are to be entered moving downward along column A starting from A2.
I want only if the adjacent values in column A are equal to each other to return TRUE.
Important case: If i was entering data in column A, the first instance of a new value for example letter B,
so it shall return false in the first time, but when i provide afterwards in its adjacent below cell value B than all is to be returned true for both B values.
Another example, in cell A13 when i entered letter C, it shall return false at its first instance, only when i enter afterwards letter C
in A14 then both shall be true.
Please refer to my excel sheet, because it is much clearer.
Thanks a lot.

All solutions worked great, but i have still only a last adjustment, in case i entered in cell A14 letter A, i shall return False and not True, because letter A has already recieved a true Score before.
In that case it will works totally right for me, thanks a lot.

Hey glen, yes, the past letters of A are ought to remain true, from cell A2 to cell A5, those letters would not change afterwards, but if an A has pop up in another cell that is not adjacent to the initial A's then it should return False, as in my case if A14 is A and A13 is not A, then A14 is false, thanks man