What is the inverse of the 3x3 matrix mod 26

1. The problem statement, all variables and given/known data

What is the inverse of the 3x3 matrix mod 26?

K = [tex]

\begin{pmatrix}

17 & 17 & 5\\

21 & 18 & 21\\

2 & 2 & 19

\end{pmatrix}

[/tex]









2. Relevant equations







3. The attempt at a solution

So I found all the cofactors and then took the transpose of the matrix. I then divided new matrix, by the determinate -939. After which I would multiply this by 17 because 23^-1 mod 26 = 17 to get the inverse. I found 17 by using the euclidean algorithm. This was all UPLOADED. However I am confused because even if I do this I do not get the answer in the book. They get:



[tex]

\begin{pmatrix}

4 & 9 & 15\\

15 & 17 & 6\\

24 & 0 & 17

\end{pmatrix}

[/tex]



I have so far without multiplying it by 17:



[tex]

\begin{pmatrix}

300/-939 & -313/-939 & 267/-939\\

-357/-939 & 313/-939 & -252/-939\\

6/-939 & 0 & -51/-939

\end{pmatrix}

[/tex]



I realize that even if I go ahead I will not reach what the book has, what have I done wrong? All of my work has been UPLOADED.

Attached Images

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