We consider unimodular matrices $M$ such that neither $M$ nor $M^{-1}$ contain zero entries. Matrices typically exhibit a trade-off: small $M$ imply large $M^{-1}$. We investigate rare cases where both remain small, classify these matrices up to symmetry, and discuss aspects of this balanced setting.

翻译：我们考虑幺模矩阵$M$，使得$M$与$M^{-1}$均不含零元素。矩阵通常存在一种权衡：小$M$意味着大$M^{-1}$。我们研究两者均保持较小的罕见情形，对这些矩阵进行对称性分类，并讨论这种平衡情形下的相关方面。