###### Exercise9

For each of the following matrix transformations, describe the eigenvalues and eigenvectors of the corresponding matrix $$A\text{.}$$

1. A reflection in $$\real^2$$ in the line $$y=x\text{.}$$

2. A $$180^\circ$$ rotation in $$\real^2\text{.}$$

3. A $$180^\circ$$ rotation in $$\real^3$$ about the $$y$$-axis.

4. A $$90^\circ$$ rotation in $$\real^3$$ about the $$x$$-axis.

in-context