in col `A` I have a list of email addresses
in col `B` I want to catch duplicates, so if an email address in A appeared before I get a trigger in `B`. 
I'm using this formula which works great:
`=if(isna(match(a3,$A$2:A2,0)),"New","Duplicate")`

note that as I drag this formula, `$A$2` stays so the range grows (e.g. for cell `B51` the range will be from `$A$2:A50`)

My problem is that since column `A` updates automatically (e.g. new email addresses are added) I want column `B` to update automatically as well. I tried using Arrayformula but can't figure it out :( 
I tried both: 
`=arrayformula(if(isna(match(A3:A,$A$2:A2,0)),"New","Duplicate"))`
and
`=arrayformula(if(isna(match(A3:A,$A$2:A2:A,0)),"New","Duplicate"))`
 but they don't work. 

here's a spreadsheet with an example and my (failing) attempts to solve it
<https://docs.google.com/spreadsheets/d/1N3pFPnT452FmWa9w8EkYpIq-ZnivjoCzt5ORrNEKgLQ/edit#gid=0>