स्कूल के बाद मैं माँ के साथ बाज़ार जाऊँगी।

Because the speaker is female.

The verb जाना means to go. In the simple future:

• मैं जाऊँगा = I will go (said by a male speaker)
• मैं जाऊँगी = I will go (said by a female speaker)

So जाऊँगी agrees with the speaker, not with माँ or बाज़ार.

The dictionary form is जाना = to go.

In this sentence, जाऊँगी is a future form built from that verb. A useful set is:

• मैं जाऊँगा / जाऊँगी = I will go
• तू जाएगा / जाएगी
• तुम जाओगे / जाओगी
• वह जाएगा / जाएगी
• हम जाएँगे / जाएँगी

So जाऊँगी specifically means will go for a female I.

Because Hindi usually uses postpositions, not prepositions.

In English, we say after school, with after before the noun.
In Hindi, the equivalent structure is:

• स्कूल के बाद = school + ke + after

Here, के बाद means after.
So literally it is something like school's after, but naturally it means after school.

के is part of the postpositional phrase के बाद = after.

Many Hindi postpositions need the noun before them to appear in the oblique form. With a noun like स्कूल, that form often looks the same, but the postposition still appears:

• स्कूल के बाद = after school
• खाने के बाद = after eating / after the meal
• काम के बाद = after work

So it is best to learn के बाद as one unit meaning after.

के साथ means with.

So:

• माँ = mother
• माँ ke साथ = with mother

This is another postpositional phrase, like के बाद.

Examples:

• दोस्त के साथ = with a friend
• परिवार के साथ = with family
• मेरे साथ = with me

So माँ के साथ means with my mother or with mother, depending on context.

Because Hindi often leaves out possessives when they are obvious from context.

So both of these can work:

• माँ के साथ = with माँ / with my mother
• मेरी माँ के साथ = with my mother

In many family-context sentences, Hindi naturally omits my, your, etc. if the relationship is clear.

Because Hindi often does not use a separate word for to with destinations after verbs of motion like go.

So:

• मैं बाज़ार जाऊँगी = I will go to the market
• वह घर जाएगा = he will go home
• हम दिल्ली जाएँगे = we will go to Delhi

English needs to in many of these cases, but Hindi usually does not.

Because destinations with जाना usually appear without को.

For example:

• मैं स्कूल जाऊँगा = I will go to school
• वह बाज़ार जाएगी = She will go to the market
• हम शहर जाएँगे = We will go to the city

Using को here would usually sound unnatural in standard Hindi.

Hindi word order is flexible, though the neutral order here is very natural:

• स्कूल के बाद मैं माँ के साथ बाज़ार जाऊँगी।

You may also hear:

• मैं स्कूल के बाद माँ के साथ बाज़ार जाऊँगी।
• मैं माँ के साथ स्कूल के बाद बाज़ार jाऊँगी।

The verb usually stays near the end.
Changing the order often changes emphasis, not basic meaning.

Yes, Hindi can often drop the subject if it is already clear.

For example:

• स्कूल के बाद माँ के साथ बाज़ार जाऊँगी।

This still means I will go to the market with माँ after school, especially because जाऊँगी already shows a female first-person speaker in context.

But including मैं makes the subject explicit and is very common.

माँ is pronounced roughly like maa, but with nasalization.

The ँ above the letter shows that the vowel is nasalized.
So it is not just plain मा; it is more like mã.

A simple learner-friendly approximation is:

• माँ ≈ maa with a soft nasal sound

A rough pronunciation is:

• जा = jaa
• ऊँ = a long oo sound with nasalization
• गी = gee

So a learner-friendly approximation is jaa-oong-ee, though in natural speech it flows together more smoothly.

The nasal sign in ऊँ adds a nasal quality.

It is a borrowed word from English school, but it is completely normal in modern Hindi.

Hindi uses many borrowed words in everyday speech.
You could also hear more Sanskrit-based vocabulary in some contexts, but स्कूल is the ordinary everyday word most people use.

It can mean both, depending on context.

In beginner translations, it is often given as market.
But बाज़ार can also carry the sense of bazaar/marketplace/shopping area.

So in this sentence, बाज़ार जाऊँगी simply means I will go to the market.

Not exactly. जाऊँगी is the simple future: I will go.

Depending on context, English may translate future meaning in different ways:

• I will go
• I’m going to go

But grammatically, the Hindi form here is a straightforward future form, not a separate going to construction.

A helpful breakdown is:

• स्कूल के बाद = after school
• मैं = I
• माँ के साथ = with माँ / with my mother
• बाज़ार = market
• जाऊँगी = will go (female speaker)

So the structure is:

time expression + subject + companion phrase + destination + verb

That is a very common Hindi pattern.