Finding the trace of the inverse of a 2x2 matrix in (mod 26)

[Woolyabyss]

Homework Statement

...(2 , 3)
A =
...(1 , 3)

Find the trace of A^(-1)

Homework Equations

(a , b)......(d , -b)
...^(-1) = (ad-bc)^(-1)*
(c , d).......(-c, a)

The Attempt at a Solution

.....(3 , -3)
A^-1 = 9*
.....(-1. 2)

(In mod 26)

... (1, -1)
=
... (-9, 18)

Trace of A^(-1) = 1 + 18 = 19The solution I was given said the trace is 18 but I can't seem to find where I went wrong.
Any help would be appreciated.
(Also sorry about the horrible way I wrote the matrices)

 

[RUber]

I don't see any issue with what you have. You can verify that your solution is the inverse, so it may be that the solution is off.