There has been some confusion about #5 in the Yatzi worksheet. To clarify, note that the curly letter D introduced in #4 is a collection of the eigenvectors you found earlier in the problem. So it is an eigenbasis.
We learned in section 7.4 that the matrix that represents P using this eigenbasis has a very special and nice form.
You may wish to refer to the pre-lecture notes I gave last Friday. I posted pictures of these notes on Moodle.