I'm a little rusty with my linear algebra, and was wondering how to prove that two matrices are similar. The question is:

Two matrices A and B are said to be similar if there exists an invertible matrix S such that $\displaystyle B = S^{-1}AS$. Prove that A ~ A.

So they want me to prove that $\displaystyle A = S^{-1}AS$, if I'm not mistaken. How do I show this? If I recall correctly, matrices are not commutative, so it's not a matter of cancelling out the S terms. Any guidance would be great!