Positive integers 1 to 9 are written in each square of a $ 3 \times 3 $ table. Let us define an operation as follows: Take an arbitrary row or column and replace these numbers $ a, b, c$ with either non-negative numbers $ a-x, b-x, c+x $ or $ a+x, b-x, c-x$, where $ x $ is a positive number and can vary in each operation.
(1) Does there exist a series of operations such that all 9 numbers turn out to be equal from the following initial arrangement a)? b)?
\[ a) \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array} )\]
\[ b) \begin{array}{ccc} 2 & 8 & 5 \\ 9 & 3 & 4 \\ 6 & 7 & 1 \end{array} )\]
(2) Determine the maximum value which all 9 numbers turn out to be equal to after some steps.
### Part (1)

To determine if there exists a series of operations such that all 9 numbers turn out to be equal from the given initial arrangements, we need to analyze the operations and their effects on the numbers.

#### Initial Arrangement a)
\[ \begin{array}{ccc} 
1 & 2 & 3 \\ 
4 & 5 & 6 \\ 
7 & 8 & 9 
\end{array} \]

1. **Sum Analysis**: The sum of all numbers in the initial arrangement is:
   \[
   1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
   \]
   If all numbers are to be equal, let that number be \( k \). Then:
   \[
   9k = 45 \implies k = 5
   \]

2. **Operation Analysis**: Each operation either decreases or increases the sum of the numbers in a row or column by \( x \). However, the sum of all numbers must remain constant at 45. Therefore, it is impossible to make all numbers equal to 5 using the given operations, as the sum would not remain constant.

#### Initial Arrangement b)
\[ \begin{array}{ccc} 
2 & 8 & 5 \\ 
9 & 3 & 4 \\ 
6 & 7 & 1 
\end{array} \]

1. **Sum Analysis**: The sum of all numbers in the initial arrangement is:
   \[
   2 + 8 + 5 + 9 + 3 + 4 + 6 + 7 + 1 = 45
   \]
   If all numbers are to be equal, let that number be \( k \). Then:
   \[
   9k = 45 \implies k = 5
   \]

2. **Operation Analysis**: Similar to arrangement a), the sum of all numbers must remain constant at 45. Therefore, it is impossible to make all numbers equal to 5 using the given operations, as the sum would not remain constant.

### Part (2)

To determine the maximum value which all 9 numbers turn out to be equal to after some steps, we need to consider the constraints of the operations and the sum of the numbers.

1. **Sum Analysis**: The sum of all numbers in any \( 3 \times 3 \) table is 45. If all numbers are to be equal, let that number be \( k \). Then:
   \[
   9k = 45 \implies k = 5
   \]

2. **Operation Constraints**: Each operation either decreases or increases the sum of the numbers in a row or column by \( x \). However, the sum of all numbers must remain constant at 45. Therefore, the maximum value which all 9 numbers can turn out to be equal to is 5.

The final answer is \( \boxed{ 5 } \)