Proof of 2D rotation commutativity

[MexicanCyber]

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.

 

[LCKurtz]

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.