Square Integer Matrix with a Single Non-Integer Entry in Its Inverse

Matrix inversion is one of the most significant operations on a matrix. For any non-singular matrix A∈Zn×n, inverse this may contain countless numbers non-integer entries. These entries could be endless floating-point numbers. Storing, transmitting, or operating such an cumbersome, especially when size n large. The only square integer that guaranteed to have as its unimodular U∈Zn×n. With property det(U)=±1, then U−1∈Zn×n UU−1=I, where I∈Zn×n identity In paper, we propose new G˜∈Zn×n, which referred almost-unimodular det(G˜)≠±1, matrix, G˜−1∈Rn×n, proven consist single entry. useful in various areas, lattice-based cryptography, computer graphics, computational problems, area large necessary, determinant required not equal ±1. Therefore, alternative