Proving Matrix Rotation: Homework Question & Attempted Solution

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The discussion centers on proving that a specific matrix represents a rotation about the origin. The original poster expresses confusion about the method to use for the proof. A suggestion is made to consider using mathematical induction, highlighting that the proof could be straightforward. The conversation also touches on calculating powers of the matrix, specifically A^2 and A^{2n}. The overall focus is on finding an effective approach to demonstrate the rotational properties of the matrix.
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Homework Statement



Untitled.png


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?
 
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Michael_Light said:

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

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