##### Exercise2

In this exercise, we will consider $$2\times 2$$ matrices as defining linear transformations.

1. Write the matrix $$A$$ that performs a $$45^\circ$$ rotation. What geometric operation undoes this rotation? Find the matrix that perform this operation and verify that it is $$A^{-1}\text{.}$$

2. Write the matrix $$A$$ that performs a $$180^\circ$$ rotation. Verify that $$A^2 = I$$ so that $$A^{-1} = A\text{,}$$ and explain geomtrically why this is the case.

3. Find three more matrices $$A$$ that satisfy $$A^2 = I\text{.}$$

in-context