Proving properties of matrices

1. Sep 13, 2011

Soluz

1) I can assume all these matrices to be 2x2.
We have matrix A and B and AB = BA, that is, they commute.. Prove if C = A^2 + 2*A and D = A^3 + 5 * I (I is identity matrix), then CD = DC.
Then give a theory that generalizes this.

2) why does R(theta)R(phi)=R(theta+phi)? (explain with "simple" words)
Knowing this, derive the formulas cos(theta + phi) and sin(theta + phi) in terms or cos(theta),cos(phi),sin(theta), and sin(phi).

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I haven't done a proof course yet so I'm completely lost.

2. Sep 13, 2011

estro

Take 2 arbitrary matrices [arbitrary values] and check what happens to these arbitrary values if the 2 matrices hold AB=BA.
Then apply it.