Proof of 2D rotation commutativity

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SUMMARY

The discussion centers on proving the commutativity of 2D rotations using matrix transformations. Participants suggest substituting trigonometric variables into two rotation matrices and calculating their products in different orders. The conclusion is that if the resulting matrices are identical, it confirms the commutative property of 2D rotations. This method is deemed sufficient for the proof.

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  • Understanding of 2D rotation matrices
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  • Knowledge of matrix multiplication
  • Basic concepts of linear algebra
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  • Research the properties of rotation matrices in 2D
  • Study the implications of matrix commutativity
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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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