Exercise 3
In the next chapter, we will say that matrices \(A\) and \(B\) are similar if there is a matrix \(P\) such that \(A= PBP^{1}\text{.}\)

Suppose that \(A\) is a \(3\times3\) matrix and that there is a matrix \(P\) such that
\begin{equation*} A = P \left[\begin{array}{rrr} 2 \amp 0 \amp 0 \\ 0 \amp 5 \amp 0 \\ 0 \amp 0 \amp 3 \\ \end{array}\right] P^{1}\text{.} \end{equation*}Find \(\det A\text{.}\)
Suppose that \(A\) and \(B\) are matrices and that there is a matrix \(P\) such that \(A=PBP^{1}\text{.}\) Explain why \(\det A = \det B\text{.}\)