Geodesic
A Diophantine problem concerning third order matrices
Serdica Mathematical Journal, Tome 47 (2022) no. 2, pp. 153-160.

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In this paper we find a third order unimodular matrix, none of whose entries is \(1\) or \(-1\), such that when each entry of the matrix is replaced by its cube, the resulting matrix is also unimodular. Further, we find third order square integer matrices \((a_{ij})\), none of the integers \(a_{ij}\) being \(1\) or \(-1\), such that \(\det{(a_{ij})}=k\) and \(\det{(a_{ij}^3)}=k^3\), where \(k\) is a nonzero integer.
Keywords: unimodular matrix, third order matrix, third order determinant, 15B36, 11C20, 11D25, 11D41 
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     title = {A {Diophantine} problem concerning third order matrices},
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Choudhry, Ajai. A Diophantine problem concerning third order matrices. Serdica Mathematical Journal, Tome 47 (2022) no. 2, pp. 153-160. http://geodesic.mathdoc.fr/item/SMJ2_2022_47_2_a4/