# Smith Normal Form of a companion matrix of monic polynomial

Let $$C(f)$$ be the companion matrix of a monic polynomial $$f(t)\in \mathbb{F}[t]$$. I need to show that the Smith Normal Form of $$tI - C(f)$$ is equal to the diagonal matrix $$\,diag(1,1,1,...,f(t))$$.

A little bit baffled on how to begin. I've constructed the companion matrix and written out my monic polynomial. I think there are some relationships between equivalent/similar matrices of the form $$tI-A$$ that might help. But I'm definitely scratching my head on understanding how to link the Smith Normal Form to all of this.