Hill is a poly alphabetic cryptosystem that is based on matrix calculation using finite rings.
The finite ring in the example uses 26 elements (A-Z), cause it is easier to read for us. The plain text message is converted to a matrix. the matrix and the secret matrix are used to calculate the secret message (in matrix form, but can be converted back to text, if needed). In order to calculate the decryption matrix from the secret matrix, the use of the adjunct proposition is used. the adjunct proposition
A is element of Mmm(R). AA^Ad = A^AdA = det AImIn order to invert the secret key (A) a computer is "required", cause doing it by hand is nonsense.
A^-1 = (det A)^-1A^Ad