Áttu eftir að athuga póstkassann, eða gerðir þú það í morgun?

It comes from the idiom eiga eftir að + infinitive, which means to still have left to do something, to still need to do something, or to have yet to do something.

So:

• Þú átt eftir að athuga póstkassann. = You still have to / still need to / have yet to check the mailbox.
• Áttu eftir að athuga póstkassann? = Do you still need to check the mailbox?

This is a very common Icelandic way to talk about something that has not been done yet.

Because Icelandic normally puts the finite verb first in a yes/no question.

Compare:

• Þú átt eftir að athuga póstkassann. = statement
• Áttu eftir að athuga póstkassann? = yes/no question

So this is just normal Icelandic question word order.

Yes. Áttu is the usual written form of átt þú.

So:

• átt = have (2nd person singular of eiga)
• þú = you

These combine as áttu in writing. This happens in several common verb + þú combinations in Icelandic.

Because the pattern is:

eiga eftir að + infinitive

Here:

• eiga = to own / have
• eftir = after / left
• að athuga = to check

In this construction, að introduces the infinitive verb. So að athuga means to check.

A lot of Icelandic verb patterns work this way, where að is required before the infinitive.

Athuga usually means check, examine, look into, or sometimes consider, depending on context.

In this sentence, the natural meaning is simply:

• athuga póstkassann = check the mailbox

So it is not especially formal here; it is just an everyday verb.

Because póstkassann means the mailbox, and it is the object of the verb.

Breakdown:

• póstkassi = a mailbox / mailbox (indefinite nominative)
• póstkassann = the mailbox (definite accusative)

Icelandic adds the definite article to the end of the noun, and the noun also changes form for case.

Since athuga takes a direct object, the noun appears here in the accusative, so you get póstkassann.

It is accusative singular definite.

Why? Because it is the direct object of athuga:

• athuga eitthvað = check something

So the thing being checked goes in the accusative.

This is very common in Icelandic: many verbs take an accusative object.

Gerðir þú það literally means Did you do that?

Breakdown:

• gerðir = did (past tense of gera, for you)
• þú = you
• það = that / it

Here það refers back to the action of checking the mailbox. So instead of repeating the whole verb phrase, Icelandic uses gera það, just like English can say did you do that?

So:

• eða gerðir þú það í morgun? = or did you do that this morning?

Yes, absolutely.

That would mean:

• or did you check the mailbox this morning?

It is grammatically fine and very clear. The version with gerðir þú það is just less repetitive, because the action has already been mentioned.

So the difference is mostly:

• gerðir þú það = more natural if you want to avoid repeating the whole phrase
• athugaðir þú póstkassann = more explicit

Because that part is also a yes/no question.

After eða (or), the speaker gives another possibility, but it is still phrased as a question:

• gerðir þú það í morgun? = did you do it this morning?

So the normal question order stays the same: verb + subject.

This is a very common thing learners ask.

• í morgun = this morning / earlier today
• á morgun = tomorrow

So the preposition matters a lot:

• í
  • morgun → this morning
• á
  • morgun → tomorrow

Even though both contain morgun, they are fixed expressions with different meanings.

Yes. The sentence sets up two opposite possibilities:

1. You still haven't checked the mailbox yet
2. You already checked it this morning

So the sentence is basically asking which is true.

That contrast is very natural in Icelandic:

• eiga eftir að = not done yet
• gera það / vera búinn að = already done

Yes, but it asks something slightly different.

• Áttu eftir að athuga póstkassann? = Do you still need to check the mailbox?
• Ertu búinn að athuga póstkassann? = Have you finished checking / Have you checked the mailbox already?

So:

• á eftir að focuses on something not yet done
• búinn að focuses on something already completed

They are related, but they are not the same.

A native speaker would usually understand it as a practical everyday question with two options:

• Have you still not checked the mailbox?
• Or did you already do it this morning?

The first half suggests the action may still be pending, and the second half offers an alternative explanation. It sounds natural and conversational, not especially formal.