$A$ is a $3 × 3$ matrix and $A^2=I$ then how to prove that $A$ can be diagonalized?

Asked Dec 07 '23 at 13:55

Active Dec 07 '23 at 15:37

Viewed 117 times

Just come across a lecture about eigenvalues and vectors; I don't know how to make a proof if there is no chance to use the algebraic & geometric multiplicity.

edited Dec 07 '23 at 15:37

Hannan

asked Dec 07 '23 at 13:55

th a

2

Or this? (More direct and elementary explicit diagonalization) – Anne Bauval Dec 07 '23 at 14:23
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If $A$ is complex or real, then also this question has answers. If the entries can be from a field of characteristic two, then the claim is not true in general. – Jyrki Lahtonen Dec 07 '23 at 14:26
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Also, I recommend that you read our abridged guide to new askers. Your question is arguably lacking in context and such. Basically this what a dumped homework assignment looks like. I'm not saying it is an assignment. It looks like one, and therefore it raises eyebrows. – Jyrki Lahtonen Dec 07 '23 at 14:33

$A$ is a $3 × 3$ matrix and $A^2=I$ then how to prove that $A$ can be diagonalized?

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