I want to know if this is true or not, and if yes how we can prove it. Given a group G and a map p be a 2- dimensional representation of G in to GL(2,ℂ). If there exist g, h ∈ G such that the matrices p(g) and p(h) do not commute then the representation p is irreducible.
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Is the group known to be finite? What do you know about the diagonalizability of commuting matrices? What do you know about commutation of diagonal matrices? – Jyrki Lahtonen Nov 29 '20 at 15:07
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Also, I recommend that you take a look at our guide for new askers. Your question is a little short of context. – Jyrki Lahtonen Nov 29 '20 at 15:09
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@JyrkiLahtonen could you please take a look at https://math.stackexchange.com/questions/3926383/does-there-getting-from-1-to-sqrt42-using-sqrt-alpha2-1 I gave an answer I believe is correct, but I don't know anywhere near enough to be convincing. – Will Jagy Nov 29 '20 at 15:45