On an old post related to determinants

[benoit]

Correction to previous email : the matrix must be symmetric...

Let M be a symmetric nxn matrix with integer coefficients (can be in 
any commutative ring) satisfying m(i,j)=0 if i+j is even  except when 
i=j=1  where m(1,1)=1 (1 can be replaced by any square),  then the 
determinant of M is (in absolute value) always a perfect square.
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