###### Exercise 7

Suppose that \(A = PDP^{-1}\) where

\begin{equation*}
D = \left[\begin{array}{rr}
1 \amp 0 \\
0 \amp 0 \\
\end{array}\right],\qquad
P = \left[\begin{array}{rr}
1 \amp -2 \\
2 \amp 1 \\
\end{array}\right]\text{.}
\end{equation*}

Explain the geometric effect that \(D\) has on vectors in \(\real^2\text{.}\)

Explain the geometric effect that \(A\) has on vectors in \(\real^2\text{.}\)

What can you say about \(A^2\) and other powers of \(A\text{?}\)

Is \(A\) invertible?