Entries in An Array

\[ \begin{bmatrix} 2&0&1&0&2&0\\ 0&2&0&1&2&0\\ 1&0&2&0&2&0\\ 0&1&0&2&2&0\\ 1&1&1&1&2&0\\ 0&0&0&0&0&0 \end{bmatrix} \]

In the above \( 6 \times 6 \) array, one can choose any \( k \times k \) subarray, with \( 1 < k \leq 6 \) and add \( 1 \) to all its entries. Is it possible to perform the operation a finite number of times such that all entries in the array are multiples of 3?

Note: If yes, state the number of times in which the operation is required. If no, type \( 0 \).


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