An interesting matrix problem

Revision en3, by anothermousey, 2023-01-12 12:09:40

I was wondering a problem: Is it possible to construct a n*n matrix (call it A) such that each number from 1 to n appears exactly n times and the result of A*A is a zero matrix (after modulo n*n terms in the matrix by n). I know it is obvious for odd n but how about even n?

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  Rev. Lang. By When Δ Comment
en10 English anothermousey 2023-01-24 18:10:52 8
en9 English anothermousey 2023-01-24 18:10:13 0 (published)
en8 English anothermousey 2023-01-24 18:09:59 2 (saved to drafts)
en7 English anothermousey 2023-01-24 16:50:28 0 (published)
en6 English anothermousey 2023-01-24 16:50:09 2
en5 English anothermousey 2023-01-24 14:42:32 1555 (saved to drafts)
en4 English anothermousey 2023-01-12 12:14:08 24 Tiny change: 'lt of A*A is a zero' -> 'lt of A*A (matrix multiplication) is a zero'
en3 English anothermousey 2023-01-12 12:09:40 4 Tiny change: 'mber from 0 to n-1 appears e' -> 'mber from 1 to n appears e'
en2 English anothermousey 2023-01-12 12:00:32 44
en1 English anothermousey 2023-01-12 11:24:31 261 Initial revision (published)