[Dey Sarkar Arnab]

I don't know whether I understand your method correctly or not! But please keep in mind that A is a matrix having natural no entries. So when you take out k the first row would be a rational number.

Now at last "

now we want det(A(k))=k so we want our final matrix (corresponding to the determinant) to be 1 hence it is one of the possible A(1)" it is true.

"so it is enough to find all the matrix of type A(1)" why is it true? If you are free sometime we can have a discussion over skype. Let me know.

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