help! modular arith and matrixes

Hi all!

I am trying to solve a problem which I am really puzzled with.

I need to find the number of possible matrixes A (2x2),
being A = INV(A) and knowing that det A = +/- 1 (mod 26)
I was trying using this way, but I don't figure it out how to follow.

A= (a b)
    (c d)

 INV(A)=INV(det A) ( d -b )
                   ( -c a )

then (a b) = INV(det A) . ( d -b )
     (c d) ( -c a )

Now, we have two possibilities:

if det A=1 , INV(det A)= 1

a=d
b=-b
c=-c
d=a
det A = ad-bc = 1 (mod 26)

and if det A=-1 : INV (det A) = -1

a=-d
b=b
c=c
d=-a
det A = ad-bc = -1 (mod 26)

How could I possibly "count" all the matrixes?

Any help will be highly appreciated! :)

aleterra
Received on Thu Sep 29 21:55:18 2005