Would you mind, if I suggest very small suggestion to your code?

$! will give more information regarding the type of failure

open (FILE_A, "$file_a") or die "couldn't open the file!";
>>open (FILE_A, "$file_a") or die "couldn't open the file $file_a <$!>
+!";
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close function will also fail, its better to check that as well

close (FILE_A);
>>close (FILE_A) or die "Unable to close file";
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