Step 1: Understand what the correct query needs to do.
Each employee's TeamSize should equal the number of employees who share that employee's TeamID. So we first need to count how many employees fall in each TeamID group, then attach that count back to every employee row with the matching TeamID.
Step 2: Check option (A).
The subquery B groups the Employee table by TeamID and computes COUNT(TeamID) for each group, giving TeamID 8 a count of 3, TeamID 7 a count of 2, and TeamID 9 a count of 1. The outer query joins every employee E to B using E.TeamID = B.TeamID, so each employee picks up the TeamSize of their own team. This reproduces the desired output exactly, so option (A) is correct.
Step 3: Check option (B).
This query self joins Employee as A and B, but the WHERE clause requires both A.TeamID = B.TeamID AND A.EmpID = B.EmpID. Since EmpID is the primary key, A.EmpID = B.EmpID forces A and B to be the exact same row every time, so COUNT(B.TeamID) always evaluates to 1 for every employee, regardless of their real team size. This does not match the desired output, so option (B) is incorrect.
Step 4: Check option (C).
Here the inner query groups by EmpID instead of TeamID. Since EmpID is already unique for every row (it is the primary key), grouping by it does nothing, each group has exactly one row, so COUNT(TeamID) is always 1. The result gives TeamSize = 1 for every employee, which does not match the desired output, so option (C) is incorrect.
Step 5: Check option (D).
The subquery B only selects COUNT(TeamID) AS TeamSize, grouped by TeamID, it never includes TeamID itself in the SELECT list. The outer query then tries to reference B.TeamID in the WHERE clause, but that column does not exist in B's result set. This makes the query invalid, it would fail with an unknown column error, so option (D) is incorrect.
Final Answer:
Only option (A) produces the correct TeamSize output; it is the only query that both runs correctly and matches the desired table.
\[ \boxed{\text{(A) only}} \]