I have to find the deciphering multiplier for a multiplication cipher given, Cq=Pi

Question

so q goes to i / 17 goes to 9
I plugged it into the equation 17a = 9(mod 26) then solved using the inverse of 17 to reduce so 23 (17)a = 23 (9)(mod 26)
this left me with a=207(mod 26) so I reduced 207 to 25 as the deciphering shift. I know the answer is supposed to be 15 so if anyone could point out where I'm going wrong I'd be very grateful.

Answer 1

I am not sure if I understand what you're supposed t find. But here's what I have found.

I have mod(23*17,26)=1 (and not 9), so 23 cannot be the multiplier.

I found it by trial and error, that
mod(25*17,26)=9, (encrypting)
mod(25*9,26)=17, (decrypting).
So 25 is the multiplicative key to encrypting and decryption.

Is that what you're supposed to do?

Answer 2

Yes. The math I did was correct and the deciphering multiplier is 25. The answer in my textbook was wrong and claimed it was 15, making me doubt my answer. Thank you for answering :)