Question

Suppose I have this: \[A=P_{0}\Lambda P_{0}^{-1}\]
And then there is a diagonal matrix D such that its determinant is always equals to 1:
\[det(D)=1\]
Then, for every DA,
\[DA = P \Lambda P^{-1}\]
How can I show that for the lambda, which is the eigenvalues matrix, does not change for all DA? And what is the relationship between \[P\] and \[P_{0}\]?