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

## Homework Statement

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

Find the trace of A^(-1)

## Homework Equations

(a , b)................................(d , -b)
(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 = 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)