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Lyrx [107]
3 years ago
6

Suppose that A = PDP-1 . Prove that det(A) = det(D)

Mathematics
1 answer:
daser333 [38]3 years ago
5 0

Answer:

Check.

Step-by-step explanation:

To prove it we need to know that  for two matrices A and B we have that:

det(AB) = det(A)*det(B) and det(A^{-1}) = \frac{1}{det(A)}. Now:

A = PDP^{-1}

det(A) = det(PDP^{-1})

det(A) = det(P)*det(D)*det(P^{-1})

det(A) = det(P)*det(D)*\frac{1}{det(P)}

det(A) = det(P)*\frac{1}{det(P)}*det(D)

det(A) = det(D).

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