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I'm triyng to do this exercize :

$$n \in \mathbb{N^*}, \ D_1,D_2,P \ \in \mathbb{M}_n(\mathbb{C})\ \text{with} \ D_1,D_2 \ \text{diagonals} \ \text{and} \ P \ \text{an invertible matrix}. \\\text{Let} \ A=PD_1P^{-1}, B=PD_2P^{-1}. \text{Are A and B commutative} ? $$

How is it possible to answer this without knowing more information on the matrices ?

Thanks you

Tom
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1 Answers1

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HINT: $D_1$ and $D_2$ do commute

Jonas Gomes
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  • thanks for your answer, with the information here http://math.stackexchange.com/questions/170241/when-is-matrix-multiplication-commutative I managed to proove it. – Tom Feb 16 '15 at 17:42
  • Yes, thats right. A simple matter of computation now will give you $AB=BA$ – Jonas Gomes Feb 16 '15 at 17:46