I have encountered some difficulty in determing a general formula for finding the inverse of an invertible n by n square matrix modulo p, for anything other than the 2 by 2 case. I know the determinant and p must be relatively prime, but know of no resources which give the precise general formula. I'm interested in computing inverses (modulo a given number, say 26) for the 3 by 3, 4 by 4 and general cases. Also does anyone have info on computational complexity pertaining to the strengths/weaknesses of this particular encryption scheme? In particular, in comparision to the RSA cipher, does the effectiveness of this algebraic method to prevent against 'knownplaintext' and other forms of cryptanalys increase exponentially as the size of the matrix used in encryption increases? i.e. does the advantages of using an exponentially large matrix outweigh the disadvantages associated with computing decryption keys, ease of Alice & bob to communicate etc etc...
