Consider the set of all symmetric matrices of a given size $n$ with entries lying in $\{0,1\}$ such that all diagonal entries are zeros in the matrices.

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Consider the set of all symmetric matrices of a given size $n$ with entries lying in {0,1} such that all diagonal entries are zeros in the matrices. Now how to write an algorithm that finds at least one matrix (from the set we have considered) which is similar to its inverse matrix via a permutation matrix.

For computation part, we can choose $n$ according to our convenience.

Please help regarding this. Thank you