Please show all work, step by step. Thank you so much!

2. [10] Prove the two successive 2D rotations are additive (and thus commutative), that is, show R(0]) . R(02) = R(01 + 02) [Hint: Recall the trig identities for sum of angles.] 3 [10] Matrix multiplication is generally not commutative, thus rotation in 3D are generally not commutative. Give an example of two rotations in opposite order that shows they are not commutative. [You do not need to give the matrices - you may simply describe the operations. For example, rotate the unit vector in the x direction, 45 degrees clockwise around the y axis, etc.] Give a drawing or plot of your results