На концерте она была в шляпе, а после концерта убрала шляпу в большую сумку.

Because different prepositions require different cases.

• на концерте = на

  • prepositional case
  • концерт → концерте
  • Here it means at the concert

• после концерта = после

  • genitive case
  • концерт → концерта
  • Here it means after the concert

So the noun changes because the preposition changes.

Russian often uses на with events and activities:

• на концерте = at a concert
• на уроке = in class / at the lesson
• на работе = at work
• на встрече = at a meeting

This is just the normal Russian pattern. Even though English often says at or in, Russian commonly uses на for many events.

В шляпе literally means in a hat, but in natural Russian it often means wearing a hat.

So:

• она была в шляпе = she was wearing a hat

Grammatically, this is в + prepositional case for a state or location:

• шляпа → шляпе

This is similar to other clothing expressions:

• в пальто = wearing a coat
• в очках = wearing glasses
• в куртке = wearing a jacket

Because the noun has two different grammatical roles.

1. в шляпе

   • after в in a static/state meaning
   • uses the prepositional case
   • шляпа → шляпе

2. убрала шляпу

   • here шляпу is the direct object of убрала
   • uses the accusative case
   • шляпа → шляпу

So the same word changes depending on its job in the sentence.

Because this part describes motion into the bag.

Russian uses:

• в
  • accusative = motion into
• в
  • prepositional = location in

So:

• убрала шляпу в большую сумку = put the hat into the big bag
• в большой сумке would mean in the big bag as a location, not movement into it

Compare:

• Книга лежит в сумке = The book is in the bag
• Она положила книгу в сумку = She put the book into the bag

Because большую agrees with сумку, which is:

• feminine
• singular
• accusative

The adjective has to match the noun.

So:

• dictionary form: большая сумка
• after motion with в
  • accusative: в большую сумку

This is normal adjective agreement in Russian.

Russian leaves out to be only in the present tense.

• Она в шляпе. = She is wearing a hat. / She is in a hat.

But in the past tense, Russian uses forms of быть:

• она была = she was

So:

• она была в шляпе = she was wearing a hat

That is completely normal.

Here убрала comes from убрать, which often means:

• to put away
• to remove
• to tidy away

In this sentence, убрала шляпу в большую сумку means something like:

• put the hat away into a big bag
• put the hat into a big bag

It suggests not just moving it, but putting it away after the concert.

A verb like положила would simply mean put/placed, while убрала adds the idea of putting away.

А is a conjunction. Here it links the two parts and gives a mild contrast or transition:

• На концерте она была в шляпе, а после концерта...
• At the concert she was wearing a hat, but/and after the concert...

In English, depending on context, а can sound like:

• and
• but
• whereas

Here it marks a change of situation:

• during the concert: the hat was on her
• after the concert: she put it into the bag

Yes, Russian word order is fairly flexible, but the version given is natural and clear.

Current sentence:

• На концерте она была в шляпе, а после концерта убрала шляпу в большую сумку.

This order works well because it presents:

1. the time/context first
2. then what she was like
3. then what happened afterward

You could rearrange parts for emphasis, for example:

• Она была в шляпе на концерте...
• После концерта она убрала шляпу в большую сумку.

But the original version sounds smooth and natural, especially in a narrative.

Not if you mean wearing a hat.

• в шляпе = wearing a hat
• со шляпой = with a hat

Со шляпой would usually mean she had a hat with her, not necessarily on her head.

So if the meaning is that she was dressed in it, в шляпе is the right choice.