Zoe and Nico, the most popular children's show on the channel, features, as the title suggests, two main characters: Zoe and Nico. These characters are never on screen at the same time and tell separate stories, but on similar themes. To illustrate the transition from one character to another within the same episode, the production team uses a small animation created by a graphic designer. This designer shows you their work during your internship.When transitioning from a segment featuring Zoe to a segment featuring Nico, you can see the letter Z transform into the letter N$.$ Point A$(-2,1)$ point b$(2,3)$ point c $(-2,-3)$ point d $(2,-1)$ The animation will be completed by applying the following transformation matrix:d$)$ Using the transformation matrix, transform the initial image and plot the resulting image on a Cartesian plane.e$)$ During the transition from a segment featuring Nico to a segment featuring Zoe, the inverse transformation occurs. Thus, you can see the letter N transform into the letter Z$.$ Determine the inverse of the transformation matrix. Then, verify that by using this new transformation matrix on the results obtained in $($a$),$ you indeed obtain the vectors forming the initial image.f$)$ Show through a calculation that the matrix has no eigenvalues.