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How can I prove that if A has eigenvalues then determinant of A is the product of its eigenvalues?

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  • $\begingroup$ Look at your the constant in the characteristic polynomial and use the relation between roots of equation and product of roots. $\endgroup$ – Yadati Kiran Nov 16 '18 at 18:42
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Hints:

1) Jordan Canonical Form

2) $\textrm{det}(AB) = \textrm{det}(A)\textrm{det}(B)$

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  • $\begingroup$ Can you write a full proof ? @BaronVT $\endgroup$ – alex Nov 16 '18 at 18:46

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