Here are the answers for each part:

1. No (All 3×3 matrices under matrix addition)
2. No (All 3×3 diagonal matrices under matrix multiplication)
3. Yes (All 3×3 diagonal matrices with all diagonals non-zero under matrix multiplication)
4. Yes (All 3×3 diagonal matrices with negative diagonal entries under matrix multiplication)
5. Yes (All 5×5 upper triangular matrices under matrix addition)
6. No (All 5×5 upper triangular matrices with positive diagonal entries under matrix multiplication)
7. Yes (All 5×5 upper triangular matrices with determinant 1 under matrix multiplication)
8. No (All negative real numbers under addition)
9. Yes (The set {π^n | n ∈ Z} under multiplication)
10. No (The set {7^n | n ∈ Z} under addition)

Do you want further details or have any questions?

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Related Questions:

1. What are the group axioms needed to confirm a group structure?
2. Why does matrix addition on 3x3 matrices fail to form a group?
3. How does determinant influence the group structure in matrix multiplication?
4. What properties make diagonal matrices with non-zero diagonals a group under multiplication?
5. How does the closure property apply to upper triangular matrices under matrix addition?

Tip: In matrix operations, always check for identity and inverse elements to determine if a set forms a group under a binary operation.