linear algebra question... see attachment

Question

chrisplusian · Answer

attachment

chrisplusian · Answer

Is there a way to show this using linear algebra? I have expanded it and shown through the multiplication and trig identities that it is true but it required a whole page of work, I am thinking there may be an easier way?

rock_mit182 · Answer

I guess you can use determinants

rock_mit182 · Answer

since |A| = 1

rock_mit182 · Answer

REMEMber that Cos^2 + sin^2 = 1 by trig identities

chrisplusian · Answer

@rock_mit182 a more useful identity in this case is (cos(x))^2-(sin(x))^2 = cos(2x) but my professor has pointed out that I am doing great on quizzes and tests but I am using "old" methods and need to depend on properties of linear algebra to simplify matters. So in this problem I have come to the solution, but through actually multiplying them out, and using trig identities. My question is not how to obtain an answer, but rather is there a way to do this VIA linear algebra properties that does not require me to expand the matrices using multiplication and using trig identities to verify the truth of the statement?