Hi,

Does anyone know how I can use the Cayley-Hamilton theorem to compute a high power of a matrix, for instance

A = [0, 2, 0; 1, 1, -1; -1, 1, 1]

A^1000 = ?

I know the theorem states that plugging the matrix A into its own characteristic polynomial will result in the 0 matrix, but I don't yet see how this can be used to solve this problem.