You need to use the option -f
:
$ grep -f A B
The option -F
does a fixed string search where as -f
is for specifying a file of patterns. You may want both if the file only contains fixed strings and not regexps.
$ grep -Ff A B
You may also want the -w
option for matching whole words only:
$ grep -wFf A B
Read man grep
for a description of all the possible arguments and what they do.