Η αστυνομική αρχή είναι η αρμόδια αρχή.

Because Greek uses the definite article with each noun phrase:

• Η αστυνομική αρχή = the police authority
• η αρμόδια αρχή = the competent authority

So η appears once for the subject and once for the predicate noun phrase after είναι (is). This is completely normal in Greek.

They are adjectives, and they must agree with αρχή in:

• gender: feminine
• number: singular
• case: nominative

Here, αρχή is a feminine singular noun, so the adjectives also appear in the feminine singular nominative form:

• αστυνομικός, -ή, -ό = police
• αρμόδιος, -α, -ο = competent / responsible

So:

• αστυνομική αρχή
• αρμόδια αρχή

are both feminine singular noun phrases.

Both instances of αρχή are in the nominative singular.

That is because:

• Η αστυνομική αρχή is the subject
• η αρμόδια αρχή is the predicate noun after είναι

In Greek, after the verb to be (είμαι), the noun identifying the subject is normally also in the nominative.

In Greek, adjectives often come before the noun, especially in neutral, standard phrasing:

• αστυνομική αρχή
• αρμόδια αρχή

That is the most natural order here.

Greek can sometimes place adjectives after the noun, but that usually changes the tone, emphasis, or style. For a learner, it is safest to treat adjective + noun as the default pattern in sentences like this.

Here it means police-related or police as an adjective.

Compare:

• η αστυνομικός = the police officer / policewoman (noun, depending on context)
• αστυνομική αρχή = police authority (adjective + noun)

So in this sentence, αστυνομική is not a person. It describes the noun αρχή.

Αρμόδια means competent, responsible, or having jurisdiction/authority in this context.

In official or legal language, η αρμόδια αρχή is a very common phrase meaning:

• the competent authority
• the responsible authority
• sometimes the relevant authority, depending on context

So this sentence sounds quite formal and administrative.

Greek repeats αρχή because each side is a full noun phrase:

• the police authority
• the competent authority

You could sometimes omit repeated words in conversation if the meaning is already obvious, but in formal language Greek usually keeps the full phrase. Here the repetition sounds precise and official.

Yes, very much so.

Both αστυνομική αρχή and especially αρμόδια αρχή are expressions you often see in:

• laws
• regulations
• government documents
• official notices

A more casual everyday conversation would usually phrase things differently.

A rough pronunciation is:

ee a-stee-no-mee-KEE ar-KHEE EE-ne ee ar-MO-thee-a ar-KHEE

A few helpful points:

• η is pronounced ee
• είναι is pronounced roughly EE-ne
• χ in αρχή is like the h/ch sound in German Bach or Scottish loch
• The written accent mark shows the stressed syllable:
  • αστυνομική
  • αρχή
  • είναι
  • αρμόδια

The dictionary forms are:

• η = the (feminine singular definite article)
• αστυνομικός = police; police-related
• αρχή = authority, principle, beginning
• είμαι = to be
• αρμόδιος = competent, responsible

So the sentence uses inflected forms of the adjectives, but the noun αρχή is already in its basic singular nominative form.

No. Αρχή has several meanings depending on context, including:

• authority
• principle
• beginning

For example:

• στην αρχή = at the beginning
• οι αρχές = the authorities

In your sentence, because of the adjectives αστυνομική and αρμόδια, the meaning is clearly authority.

Yes, Greek word order is more flexible than English, but the original order is the most neutral:

• Η αστυνομική αρχή είναι η αρμόδια αρχή.

If you changed it to:

• Η αρμόδια αρχή είναι η αστυνομική αρχή.

the meaning would still be similar, but the emphasis shifts. Now the sentence starts with the competent authority, and then identifies it as the police authority.

So word order can affect focus, even when the basic meaning stays close.

In standard Modern Greek, είναι is normally included in a sentence like this.

Greek does allow some omission of words in very informal speech, headlines, labels, or notes, but in a normal full sentence—especially a formal one like this—you should use είναι.

So:

• Η αστυνομική αρχή είναι η αρμόδια αρχή. = correct, complete sentence

Yes: αρμόδια does not always map neatly to just one English word.

Depending on context, you might translate the sentence as:

• The police authority is the competent authority.
• The police authority is the responsible authority.
• The police authority is the relevant authority.

In legal and bureaucratic contexts, competent authority is often the most exact translation.