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

1. Oct 31, 2014

### Woolyabyss

1. The problem statement, all variables and given/known data
.......(2 , 3)
A =
......(1 , 3)

Find the trace of A^(-1)
2. Relevant equations
(a , b)................................(d , -b)
(c , d).................................(-c, a)

3. 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 = 19

The 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)

2. Oct 31, 2014

### 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.