Hill cipher's susceptibility to cryptanalysis has rendered it unusable in practice, it still serves an important pedagogical role in both cryptology and linear algebra. Hill cipher requires inverse of the key matrix while decryption. In fact that not all the matrices have an inverse and therefore they will not be eligible as key matrices in the Hill cipher scheme. Furthermore, due to its linear nature, the basic Hill cipher succumbs to known-plaintext attacks. In order to repair these flaws of the original Hill cipher, in this paper we proposed Invertible, involutory and permutation matrix generation methods for Hill cipher system.