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Take all the $n\times n$ matrices of 0's and 1's and define an equivallence relation as follows: Two matrices are equal if there is a way to pass from the one to another by alternating the columns and the lines.(acting by$S_n$ rows.(acting by $S_n$ on the columns and on the linesrows)

Is there a good way to determine whether two such matrices are equal?

Are there any good invariants (polynomials ,etc.)?

The obvious invariant is that the sum of the 1's on the lines rows and on the columns does not change.

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# Invariants on matrices

Take all the $n\times n$ matrices of 0's and 1's and define an equivallence relation as follows: Two matrices are equal if there is a way to pass from the one to another by alternating the columns and the lines.(acting by$S_n$ on the columns and on the lines)

Is there a good way to determine whether two such matrices are equal?

Are there any good invariants (polynomials ,etc.)?

The obvious invariant is that the sum of the 1's on the lines and on the columns does not change.