This is a question on a quiz, so I'm not looking for the answer, just a pointer in the right direction.

I have the following matrix:

5 2

-1 3

I computed the characteristic polynomial and got the following eigenvalues:

(i-4) and (i+4)

Unfortunately, the matrix that I got by multiplying (i-4) by identity(3) and subtracting the original matrix reduces to identity(3) according to my calculator. (i+4) does the same.

Uuh? What are you doing here? Do you mean $\displaystyle (i\pm 4)\cdot 3I - A = 3I$ ?? And even if you get this, what are you doing it for?? What are you trying to achieve? Tonio
Can anyone help, or do I need to provide more information?