I am trying to solve a hill cypher and I have the original matrix (I'll call it H):

| 1 2 6|

| 1 4 5|

| 6 12 8|

I have tried and tried to get the decryption matrix but I am lost, this is what I have so far:

H(transpose):

| 1 1 6|

| 2 4 12|

| 6 5 8|

Then I find H(adjoint):

| -28 56 -14|

| 22 -28 1|

| -12 0 2|

Then I find the multiplicative inverse of det(H):

det(H) = -56

-56*det(H)^-1 = 1 mod 29

det(H)^-1 = 14

Now I multiply H(adjoint) with 14 resulting in

| -392 784 -196|

| 308 -392 14|

| -168 0 28|

I then take mod 29 of each number in the matrix to get H^-1 (the decryption matrix)

|14 1 7|

| 8 14 14|

| 6 0 28|

When I decrypt the a cipher text and re-encrypt it I do not get the same cipher text and plain texts so something in my calculation of the decryption matrix must be wrong. Can anyone help?