Question: The equation ending Example 2.5 is a bit jarring because for P we must take the first matrix, which is shown as an inverse, and

The equation ending Example 2.5

is a bit jarring because for P we must take the first matrix, which is shown as an inverse, and for P-1 we take the inverse of the first matrix, so that the two -1 powers cancel and this matrix is shown without a superscript -1.
(a) Check that this nicer-appearing equation holds.

(b) Is the previous item a coincidence? Or can we always switch the P and the P-1?

3 2 1 1 113 2 1

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