Question

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

Answer 1

Check.

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)) = (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)*(1)/(det(P))`

`det(A) = det(P)*(1)/(det(P))*det(D)`

`det(A) = det(D)`.