MathDB

In the following

6\times 6

matrix, one can choose any

k\times k

submatrix, with

1<k\leq6

and add

1

to all its entries. Is it possible to perform the operation a finite number of times so that all the entries in the

6\times 6

matrix are multiples of

3

\begin{pmatrix} 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{pmatrix}

Note: A

p\times q

submatrix of a

m\times n

matrix (with

p\leq m

q\leq n

) is a

p\times q

matrix formed by taking a block of the entries of this size from the original matrix.

Problem Statement