It is well known that $\exp(C^{-1}AC)=C^{-1}\exp(A)C$, where $C$ is an invertible matrix. Really,
$$\exp(A)=\sum{}\frac{A^k}{k!} \quad \text{and} \quad (C^{-1}AC)^k=C^{-1}A^kC,$$
so the first equality is obvious. The problem in the book on the representation theory is formulated as follows:
Prove that $\exp(C^{-1}AC)=C^{-1}\exp(A)C$, avoiding explicit evaluations.
How to do it? Using some simple facts from linear algebra?