Acts 21:38 οὐκ ἄρα σὺ εἶ ὁ Αἰγύπτιος

Did the Chiliarch assume an Egyptian would know Greek?
Or assume an Egyptian would not know Greek?

Many translations appear to believe that the Chiliarch assumed an Egyptian would not know Greek.
But some, like the Complete Jewish Bible, appear to believe the Chiliarch thought an Egyptian would know Greek.
Some are ambiguious or slightly implying affirmative, saying “Are you not that Egyptian?”
This is quite different from some, which say “Then you are not that Egyptian.” (See all the translations listed with their renderings, at the bottom of this post.)

But what are the rules of Greek grammar here?
The BDF grammar §440 says “οὐ is employed to suggest an affirmative answer, μή (μήτι) a negative reply; in the latter, μή with the indicative is an external indication that it is a question, since independent μή can be used in no other way than interrogatively”
So according to BDF, the correct translation here, employing οὐ, would be “Then you are that Egyptian, aren’t you.”
Combined with ἄρα DeBrunner says in §440(2) “Οὐκ ἄρα denotes astonishment in Ac. 21:38 (‘why, are you not…’), elsewhere it corresponds to ‘well’ or ‘then’. “
Hmm, why different only here, DeBrunner? I do not agree. I think the Chiliarch is saying, “Then aren’t you that Egyptian?” and assuming an affirmative answer, since that is the grammar.
BDAG says it means “are you not, then…” With ἄρα being inferential or consequential. (With οὐ suggesting an affirmative answer of course.)

I conclude that those translations which render it “then you are not that Egyptian” or, “I thought you were that Egyptian” are incorrect. And it is apparent to me, that the Roman commander assumed an Egyptian would know Greek. To read my translation of this verse, you can download my translation.

KJ21 Art not thou that Egyptian…?
ASV Art thou not then the Egyptian…?
AMP Then you are not [as I assumed] the Egyptian…?
AMPC Are you not then [as I supposed] the Egyptian…?
BRG Art not thou that Egyptian…?
CBW Are you not the Egyptian…?
CSB Aren’t you the Egyptian…?
CEB Aren’t you the Egyptian…?
CJB Say, aren’t you that Egyptian…?
CEV Aren’t you that Egyptian…?
DARBY Thou art not then that Egyptian?
DLNT Then are you not the Egyptian…?
DRA Art not thou that Egyptian…?
ERV Then you are not the man I thought you were. I thought you were the Egyptian.
EHV Are you not the Egyptian…?
EMTV Are you not then the Egyptian…?
ESV Are you not the Egyptian, then…?
ESVUK Are you not the Egyptian, then…?
EXB I thought you were [L Are you not…?] the Egyptian.
GNV Art not thou the Egyptian…?
GW Aren’t you the Egyptian…?
GNT Then you are not that Egyptian…?
HCSB Aren’t you the Egyptian…?
ICB I thought you were the Egyptian.
ISV You’re not the Egyptian…are you?
PHILLIPS Aren’t you that Egyptian…?
JUB Art not thou that Egyptian…?
KJV Art not thou that Egyptian…?
AKJV Art not thou that Egyptian…?
LAMSA Are you not that Egyptian…?
LEB Then you are not the Egyptian…?
TLB Aren’t you that Egyptian…?
MSG I thought you were the Egyptian.
MEV Are you not the Egyptian…?
MOUNCE Then you are not the Egyptian…?
MURD Art not thou that Egyptian…?
NOG Aren’t you the Egyptian…?
NABRE So then you are not the Egyptian…?
NASB Then you are not the Egyptian…?
NCV I thought you were the Egyptian.
NET Then you’re not that Egyptian…?
NIRV Aren’t you the Egyptian…?
NIV Aren’t you the Egyptian…?
NKJV Are you not the Egyptian…?
NLV Are you not the man from the country of Egypt…?
NLT Aren’t you the Egyptian…?
NMB Are you not that Egyptian…?
NRSV Then you are not the Egyptian…?
NTE Aren’t you the Egyptian…?
OJB Then you are not the Egyptian…?
TPT Aren’t you that Egyptian…?
Recov You are not then the Egyptian…?
RSV Are you not the Egyptian, then…?
TLV Then you’re not the Egyptian…?
VOICE We thought you were that Egyptian.
WEB Aren’t you then the Egyptian…?
WE I thought you were the man from the country of Egypt.
WYC Whether thou art not the Egyptian…?
YLT art not thou, then, the Egyptian…?