$(8$ points$)$ A thief enters a shop and threatens the clerk, forcing him to open the safe. The clerk says, 'The code for the safe is changed every day, and if you hurt me you'll never get the code". The code was encrypted using the matrix $A=\left[\begin{array}{cc}2& 3\\ 1& 7\end{array}\right]$ in a Hill $2-$cipher, and the result is: DGRUCPTF

$($a$)$ Find the decryption matrix $A^{-1}.$

For easy reference, here are the reciprocals modulo $26$ :

$\backslash$table$[[a,1,3,5,7,9,11,15,17,19,21,23,25],[a^{-1},1,9,21,15,3,19,7,23,11,5,17,25]]$

$($b$)$ Use matrix multiplication to verify your answer to part $($a$).$

$($c$)$ Decode the message the thief used to open the safe $($which he claims he got from the clerk$).$ For easy reference, here are the numbers corresponding to each letter of the alphabet:

$\backslash$table$[[A,B,C,D,E,F,G,H,$I,$J,K,L,M,N,O,P,Q,R,S,T,U,V,W,x,Y,Z$