Proving Matrix Rotation: Homework Question & Attempted Solution

[Michael_Light]

Homework Statement

Homework Equations

The Attempt at a Solution

I understand that matrix in the form of A as above represents a rotation about the origin.. but for this question, I am actually clueless on what method should i use to prove it... Any hint?

 

[Mark44]

Homework Statement

View attachment 56742

Homework Equations

The Attempt at a Solution

I understand that matrix in the form of A as above represents a rotation about the origin.. but for this question, I am actually clueless on what method should i use to prove it... Any hint?

Seems like a natural for an induction proof.

 

[HallsofIvy]

It looks to me to be almost trivial! What is $A^2$? $A^{2n}= (A^2)^n$.