My Algebra teacher made that statement and asked why it was true. I am not able to formulate a correct demonstration. I thought of something using Det (AB) = Det (A). Det (B) but I think I'm wrong.
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What exactly does "$\Bbb R$" mean? You need to be a bit more specific if this problem is to make enough sense to be answerable. – Arthur Mar 12 '21 at 20:18
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Sorry, I edited – Mar 12 '21 at 20:20
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That's still not entirely enough. $\Bbb R$ is a set. Presumably you want a group. Which group exactly is it that you want? Being clear about these things is a good first step to an answer, whether you want to find it yourself or want someone else to help you. – Arthur Mar 12 '21 at 20:20
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Right, I understand – Mar 12 '21 at 20:26
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In fact you’re absolutely right!
The formula $$\det AB = \det A \det B$$ is exactly saying that $\det$ is an homomorphism between the groups $(GL_n(\mathbb R), \times)$ and $(\mathbb R^*, \cdot)$.
mathcounterexamples.net
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I thought it was very simple, however, according to the definition of homomorphism and the formula I tried to use, things made sense. – Mar 12 '21 at 20:22
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@Arthur Thanks for noticing the typos... hopefully fixed. – mathcounterexamples.net Mar 12 '21 at 20:24
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