1. The problem statement, all variables and given/known data Given the following matrix A = [3 -1; -1 3] Find C = (0.5*A - I)100 2. Relevant equations Using the knowledge that the Cayley - Hamilton Theorem must satisfy its own characteristic polynomial. 3. The attempt at a solution Here the characteristic polynomial is λ2 - 6*λ + 8. When we plug in A = λ we can verify that the solution A2 - 6*A + 8 = 0 which it does. If I solve by hand/brute force way, I get C = [0.5 -0.5; -0.5 0.5] regardless of what the exponential is (here the exponential is 100). As far as applying the Cayley-Hamilton theorem, I am not connecting the two. I understand how to solve for A^3 or A^4, √A, or exp(A) but not for this problem. Any help in the right direction will be greatly appreciated.