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Skewed Commutative (?) Matrix (1)

Introduction to Linear Algebra by Gilbert Strang
Chapter 2, Section 4, Problem 22

Abstract

``By trial and error find real nonzero 2 by 2 matrices such that DE = -ED (not allowing DE = 0)'' is a problem 22, Chapter 2, Section 4 in Introduction to Linear Algebra 4th ed. by Gilbert Strang. When I worked on this problem, I got another question. ``How many such matrix pairs are there?'' I computed it and got an answer 56. Then I talk about this with my friend Marco, he asked me another question, ``Can we visualize them?'' Here is my answer of his question.


Linear Algebra, 2.4, Problem 22
There are many interesting questions in the book, Introduction to Linear Algebra 4th ed. by Gilbert Strang. For example, in Chapter 2, Section 4, Problem 22 is

 By trial and error find real nonzero 2 by 2 matrices such that
 A^2 = -I, BC = 0, DE = -ED (not allowing DE = 0).
By trial and error, I found the following answer.

Equation(1)

The book's solution page has a different answer with a comment, ``You can find more examples (p.521).''

Then I thought that How many such matrix pairs were there.

To to continued....
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