correct prepositions

  1. The detective looked into the murder.
    1a. The detective looked into the murder case.
  2. Please look into the matter.
    2a. Please look in the matter.
  3. He jumped into the river.
    3a. He jumped in the river.
  4. He jumped into the pool.
    4a. He jumped in the pool.
    Please choose the right sentences.

I find 1,2,3 and 4 to be marginally better. If you’re already in the river, and you start jumping (which would require a shallow river), you’re jumping in the river, but jumping into the river indicates that you are entering the water. Like I said, it’s pretty marginal. If you say “in”, most people will assume that it’s a jump into.