Let $n$ be a positive integer. Nancy is given a rectangular table in which each entry is a positive integer.  She is permitted to make either of the following two moves:

(1)  select a row and multiply each entry in this row by $n$;

(2)  select a column and subtract $n$ from each entry in this column.

Find all possible values of $n$ for which the following statement is true:

Given any rectangular table, it is possible for Nancy to perform a finite sequence of moves to create a table in which each entry is $0$.
1. **Initial Consideration for \( n = 1 \):**
   - If \( n = 1 \), the first move (multiplying a row by \( n \)) does not change the entries since multiplying by 1 leaves the entries unchanged.
   - The second move (subtracting \( n \) from each entry in a column) subtracts 1 from each entry in the column.
   - If the entries in a column are not all equal, subtracting 1 repeatedly will never make all entries zero simultaneously. Therefore, \( n = 1 \) does not work.

2. **Consideration for \( n > 2 \):**
   - Suppose \( n > 2 \). Consider a table with a single column containing the entries 2 and 1.
   - Multiplying the row containing 2 by \( n \) results in \( 2n \), and multiplying the row containing 1 by \( n \) results in \( n \).
   - Subtracting \( n \) from the column entries will not make both entries zero simultaneously because the two values \( 2n \) and \( n \) are not congruent modulo \( n-1 \). Specifically, \( 2n \equiv n \pmod{n-1} \) simplifies to \( n \equiv 0 \pmod{n-1} \), which is not possible unless \( n = 1 \), which we have already ruled out.
   - Therefore, \( n > 2 \) does not work.

3. **Consideration for \( n = 2 \):**
   - We need to show that for \( n = 2 \), it is possible to make all entries in the table zero using the allowed moves.
   - Consider any column with two entries \( a \) and \( b \). We can perform the following steps:
     - Multiply the row containing \( a \) by 2, resulting in \( 2a \).
     - Subtract 2 from the column containing \( 2a \) and \( b \) repeatedly until one of the entries is 2. This is possible because subtracting 2 repeatedly will eventually reduce any positive integer to 2.
     - Once one of the entries is 2, double it to get 4, and then subtract 2 repeatedly until both entries are 2.
     - Now, both entries are equal, and we can treat them together. We can continue this process for the rest of the column.
   - By repeating this process for each column, we can make all entries in the table zero.

Conclusion:
- The only value of \( n \) for which it is possible to make all entries in the table zero using the allowed moves is \( n = 2 \).

The final answer is \( \boxed{ n = 2 } \).