the follow cryptogram was encoded with a 2 X 2 matrix
5,2,25,11,-2,-7,-15,32,14,-8,-13,38,19,-19,-19,37,16

the last word of the message is -Sue what is the message?

I am not sure what 2 by 2 matrix to use? 

--------------------------------------------------------

You accidentally left out a number in the message and
that caused me to have to go to a lot of trouble to 
discover what number you left out. But I finally
found it.  You left out the number -30 between the
-15 and the 32. 

You had this:

5,2,25,11,-2,-7,-15,32,14,-8,-13,38,19,-19,-19,37,16

and it should have been this:

5,2,25,11,-2,-7,-15,-30,32,14,-8,-13,38,19,-19,-19,37,16

Make that as this list of 1 by 2 matrices:

[5 2],[25 11],[-2 -7],[-15 -30],[32 14],[-8 -13],[38 19],[-19 -19],[37 16]

Let a blank space "_" be 0, let A be 1, B be 2, etc. In other
words:

_=0, A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, I=9, J=10, K=11,
L=12, M=13, N=14, O=15, P=16, Q=17, R=18, S=19, T=20, U=21,
V=22, W=23, X=24, Y=25, Z=2600

Let the decoding matrix (the inverse of the coding matrix) be

[a   b]
[     ]
[c   d]

Don't confuse the small letters a,b,c,d with the capital letters
A,B,C,D as they are different.

Since _=0, S=19, U=21, and E=5

The last two 1 by 2 matrices in the 
coded message 

[-19 -19], [37 16]

must decode as the numbers corresponding to

[- S],[U E] 

which are

[0 19],[21 5]

So [19, -19]must decode to [_ S], or [0, 19]

Therefore,

          [a    b] 
[-19 -19]·[      ] = [0 19]
          [c    d]

Multiplying the matrices on the left:

[-19a-19c   -19b-19d] = [0 19]

So we have the equations

-19a-19c = 0
-19b-19d = 19

Also 37, 16 must decode to U, E, or 21, 5

        [a    b] 
[37 16]·[      ] = [21 5]
        [c    d]

Multiplying the matrices on the left:

[37a+16c   37b+16d] = [21 5]

So we have the equations

37a+16c = 21
37b+16d =  5

So we have the four equations:

-19a-19c = 0
-19b-19d = 19
 37a+16c = 21
 37b+16d = 5

Solving the 1st and 3rd

-19a-19c = 0
 37a+16c = 21

that gives a=1 and c=-1

Solving the 2nd and 4th

-19b-19d = 19
 37b+16d = 5

that gives b=1 and d=-2

So the DEcoding matrix is

[a   b]   [1   1]
[     ] = [     ]
[c   d]   [-1 -2]

So we start decoding

[5 2],[25 11],[-2 -7],[-15 -30],[32 14],[-8 -13],[38 19],[-19 -19],[37 16]

Decoding the [5 2]

       [1   1]
  [5 2][     ] = [5-2  5-4] = [3 1] = [C A]
       [-1 -2]

Decoding the [25 11]

        [1   1]
 [25 11][     ] = [25-11  25-22] = [14 3] = [N C]
        [-1 -2]

Decoding the [-2 -7]

        [1   1]
 [-2 -7][     ] = [-2+7 -2+14] = [5 12] = [E L]
        [-1 -2]

Decoding the [-15 -30]


         [1   1]
[-15 -15][     ] = [-15+15  -15+30] = [0 15] = [_ O]
         [-1 -2]

Decoding the [32 14]


         [1   1]
  [32 14][     ] = [32-14  32-28] = [18 4] = [R D]
         [-1 -2]

Decoding the [-8 13]


          [1   1]
  [-8 -13][     ] = [-8+13 -8+26] = [5 18] = [E R]
          [-1 -2]

Decoding the [38 19]

          [1   1]
   [38 19][     ] = [38-19 38-38] = [19 0] = [S _]
          [-1 -2]

And of course  [-19 -19] decodes as [_ S] and

[37 16] decodes as [U E}

so the decoded message is

[C A},{N C],[E L],[_ O],{R D],[E R],[S _],[_ S], [U E]  

CANCEL_ORDERS_ _SUE

Edwin