Learn Hardcore Malay: Saya simpan jemputan itu di dalam dompet saya.

So the normal pattern is: noun + ini/itu, not ini/itu + noun.
Putting itu before the noun would sound unnatural in standard Malay (itu jemputan is only used in special emphatic or spoken contexts).

What is the difference between jemputan and undangan?

Both can mean invitation, but there are some preferences and nuances:

jemputan
- Very common in Malaysia.
- From the verb jemput (to invite).
- Used in both everyday and formal contexts.
undangan
- More strongly associated with Indonesian, though Malaysians do understand it.
- Feels a bit more formal/literary in Malay, and much more standard in Indonesian.

In the sentence you gave, jemputan is the most natural choice in everyday Malaysian Malay. In Indonesian, undangan would be very typical: Saya menyimpan undangan itu di dalam dompet saya.

Why do we say di dalam dompet saya instead of just dalam dompet saya or di dompet saya? Are they all correct?

All three are grammatically possible, but they differ slightly in style and nuance:

di dalam dompet saya
- Literally in the inside of my wallet.
- Sounds a bit more explicit or slightly more formal.
- Often used in writing or when you want to be clear about something being inside.
dalam dompet saya
- Also in my wallet.
- Very natural and common in speech.
- Slightly shorter and more casual.
di dompet saya
- Literally at/on my wallet, but in practice often understood as in my wallet depending on context.
- Can sound a bit less precise than di dalam / dalam if you really mean physically inside.

In everyday conversation, Saya simpan jemputan itu dalam dompet saya would be very natural. The version with di dalam is perfectly correct and just a bit more explicit.

Can I drop the second saya and just say Saya simpan jemputan itu di dalam dompet?

You can, and people will understand you, but there’s a small difference:

di dalam dompet saya = in my wallet (clearly your wallet)
di dalam dompet = in (a/the) wallet (whose wallet is it? Not specified)

Because Malay has no articles (a/the), dropping saya makes the phrase less specific.
If context already makes it obvious that the wallet is yours, speakers might omit saya in casual speech, but the more complete and natural sentence here is di dalam dompet saya.

Can I use aku instead of saya? What changes in meaning or tone?

Yes, grammatically you can replace saya with aku:

Saya simpan jemputan itu di dalam dompet saya.
Aku simpan jemputan itu di dalam dompet aku.

The difference is in formality and politeness:

saya
- Polite, neutral, standard.
- Used with strangers, in formal situations, with older people, at work, etc.
aku
- More intimate, casual, or informal.
- Used with close friends, family (depending on family culture), or in informal speech.

Match the possessive pronoun too:
If you use saya, use dompet saya.
If you use aku, it’s more natural to use dompet aku.

Why is the verb simpan used instead of menyimpan? Aren’t Malay verbs supposed to take meN- prefixes?

The base verb is simpan (to keep, to store). The meN- form is menyimpan.

In standard written Malay, you will often see:

Saya menyimpan jemputan itu di dalam dompet saya.

In everyday speech, however, it is very common and natural to use the bare verb without the prefix:

Saya simpan jemputan itu di dalam dompet saya.

So:

menyimpan = more formal/standard, typical in writing, speeches, exams.
simpan (as a finite verb) = very common in spoken Malay, informal writing, and still generally accepted.

Both are correct; the sentence you have is just in a more spoken/neutral style.

How do we know whether simpan here means kept, keep, or will keep? There’s no tense marker.

Malay verbs do not change form for tense. Simpan by itself is time-neutral:

saya simpan can mean:
- I keep / I am keeping / I kept / I will keep — depending on context.

To make the time more explicit, Malay uses time words:

Past:
- Saya sudah simpan jemputan itu… (I have already kept…)
- Tadi saya simpan jemputan itu… (Earlier I kept…)
Present / habitual:
- Sekarang saya simpan jemputan itu… (Now I keep/am keeping…)
- Saya selalu simpan jemputan itu… (I always keep…)
Future:
- Nanti saya akan simpan jemputan itu… (Later I will keep…)

In isolation, Saya simpan jemputan itu di dalam dompet saya is often understood as past or present, depending on the context of the conversation.

Is the word order fixed? Can I say Jemputan itu saya simpan di dalam dompet saya?

Yes, you can move jemputan itu to the front:

Saya simpan jemputan itu di dalam dompet saya.
Jemputan itu saya simpan di dalam dompet saya.

Both are grammatical. The difference:

Saya simpan jemputan itu…
- Neutral subject–verb–object order.
- Slight focus on the subject saya (I).
Jemputan itu saya simpan…
- Brings jemputan itu to the front for emphasis or topic: That invitation, I kept it in my wallet.
- Common in spoken Malay to highlight the object/topic.

Word order in Malay is fairly flexible for emphasis, but the original order is the most neutral and straightforward.

What’s the difference between simpan and letak? Could I say Saya letak jemputan itu di dalam dompet saya?

You could say Saya letak jemputan itu di dalam dompet saya, and people will understand you, but the nuance is different:

simpan
- to keep, to store, to put away for safekeeping
- Implies you intend to keep it there, to preserve it.
- Very natural for things like invitations, documents, money, etc.
letak
- to put, to place, to set down (somewhere)
- Emphasizes the act of placing, not necessarily for safekeeping.
- Often used for objects you just place down:
  - Saya letak buku itu atas meja. (I put the book on the table.)

In your sentence, simpan is more appropriate because you are “keeping” the invitation safely in your wallet.

Why is there no word for “the” in this sentence? How do we know it’s the invitation and not just an invitation?

Malay does not have articles like a/an or the. Instead, definiteness is shown by:

Context
- If both speakers know which invitation is being discussed, jemputan can be understood as the invitation.
Demonstratives ini / itu
- jemputan itu = that invitation / the invitation (that we both know about)
- jemputan ini = this invitation

In your sentence, jemputan itu naturally corresponds to that invitation or the invitation, because itu points to a specific, known invitation.

Could I say di dompet saya instead of di dalam dompet saya?

Yes, di dompet saya is grammatically correct and commonly used. In many everyday contexts it still means in my wallet, because people infer that meaning.

But there is a subtle difference:

di dalam dompet saya = inside my wallet (explicitly inside)
di dompet saya = literally at/on my wallet, but usually understood as in my wallet in real use

If you want to be very clear that something is physically inside, dalam / di dalam is safer.
In casual speech, you will often hear dalam dompet saya or dalam dompet aku.

Does dompet always mean wallet? Can it also mean a women’s purse or handbag?

In modern everyday Malay:

dompet usually means wallet, for both men and women (the small thing that holds money/cards).
A larger handbag/purse (the bag you carry) is more often called beg tangan or just beg.

So dompet in your sentence is best understood as wallet.
If you wanted to say I kept the invitation in my handbag, you’d say:

Saya simpan jemputan itu di dalam beg tangan saya.

How would I say “the invitations” in the plural? Do I need to change jemputan?

Malay does not usually mark plural on the noun itself. Jemputan can mean invitation or invitations depending on context.

To make it clearly plural, you can add a quantifier or a plural marker:

jemputan-jemputan itu (reduplication, more formal/written)
semua jemputan itu = all those invitations
beberapa jemputan = several invitations

For your sentence in plural:

Saya simpan semua jemputan itu di dalam dompet saya.
= I kept all those invitations in my wallet.