##### Exercise7

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*}
1. Explain the geometric effect that $$D$$ has on vectors in $$\real^2\text{.}$$

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

3. What can you say about $$A^2$$ and other powers of $$A\text{?}$$

4. Is $$A$$ invertible?

in-context