This puts folder A into folder B:
bash rsync -avu --delete "/home/user/A" "/home/user/B"
If you want the contents of folders A and B to be the same, put /home/user/A/ (with the slash) as the source. This takes not the folder A but all of its content and puts it into folder B. Like this:
bash rsync -avu --delete "/home/user/A/" "/home/user/B"
-a Do the sync preserving all filesystem attributes
-v run verbosely
-u only copy files with a newer modification time (or size difference if the times are equal)
–delete delete the files in target folder that do not exist in the source