Proof of 2D rotation commutativity

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2D rotations via matrix transformations are commutative, meaning the order of rotation does not affect the final result. Substituting trigonometric variables into the rotation matrices and computing them in different orders can demonstrate this property. The calculations will yield the same resultant matrix, confirming the commutativity of the rotations. This method is deemed sufficient for proving the concept. Understanding this principle is essential in linear algebra and applications involving rotations.
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Homework Statement



How is it possible to prove that 2-dimensional rotations (via matrix transformations) are commutative?


Homework Equations





The Attempt at a Solution



I believe subbing in trig variables in two matrices and then calculating them in different orders would result in the same matrix and prove it, but I am not sure it is sufficient.
 
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MexicanCyber said:

Homework Statement



How is it possible to prove that 2-dimensional rotations (via matrix transformations) are commutative?

I believe subbing in trig variables in two matrices and then calculating them in different orders would result in the same matrix and prove it, but I am not sure it is sufficient.

Yes, that would prove it.
 

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