I think you've already articulated a very basic psuedocode for the issue you describe in stating that you wish to delete duplicate values from column A.
For this example, I would tend to;
Find all instances of duplicates
Work out method of determining which one to keep (Google "MAX N in
Group" for ideas) There are good articles here on SO and DBA
Stackexchange also other external articles with examples
Write your delete to cater for the records you identify as unwanted
duplicates in the previous step
For me, when working through these types of issues in SQL Server, I tend to write a series of Common Table Expressions (CTE) to identify my target records and then delete based on that.
For example;
;WITH Duplicates AS (
-- Write your select query to identify which subset of your records are affected by having duplicate values in Column A
), TargetRows AS (
-- Further select from Duplicates some method of MAX N in Group to identify which of the rows are unwanted
) -- Then here DELETE from your table based upon your findings from above