"Given operators σ,τ on a finite-dimensional space V, show that στ=i, and that σ=p(τ) for some polynomial p in F[x]."(adsbygoogle = window.adsbygoogle || []).push({});

The first part was no problem. As for the second, I have a strong suspicion that p is the characteristic polynomial, mostly because I believe I heard of that fact before (that a matrix inserted into its own characteristic polynomial it its inverse). However, I can't seem to find anything about that, and furthermore, the characteristic polynomial has not yet been mentioned in the text I'm using.

Any idea how the proof should proceed?

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# Characteristic polynomial

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