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 [tex]det(A^{-1}) = \frac{1}{det(A)}[/tex]. Now:
[tex]A = PDP^{-1}[/tex]
[tex]det(A) = det(PDP^{-1})[/tex]
[tex]det(A) = det(P)*det(D)*det(P^{-1})[/tex]
[tex]det(A) = det(P)*det(D)*\frac{1}{det(P)}[/tex]
[tex]det(A) = det(P)*\frac{1}{det(P)}*det(D)[/tex]
[tex]det(A) = det(D)[/tex].
