Solution to Exercise 3.63.
I had a feeling once about Mathematics  that I saw it all. Depth beyond depth was revealed to me  the Byss and Abyss. But it was after dinner and I let it go.
—Sir Winston Churchill (1874–1965)

Exercise 3.63. What is the form of the inverse of an affine translation of the Euclidean plane? Affine rotation?

Let  be the matrix of an affine translation of the Euclidean plane by the vector PQ = (a, b, 0). Then

 

Let  be the matrix of an affine rotation of the Euclidean plane about the origin. Then