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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