###### Exercise 9

Suppose that \(A\) is a matrix and there is an invertible matrix \(P\) such that

\begin{equation*}
A = P~\left[\begin{array}{rrr}
2 \amp 0 \amp 0 \\
0 \amp -3 \amp 0 \\
0 \amp 0 \amp 1 \\
\end{array}\right]~P^{-1}\text{.}
\end{equation*}

What can you conclude about \(\nul(A)\text{?}\)

What can you conclude about \(\col(A)\text{?}\)