In general, matrix multiplication is not commutative (i.e., AB BA). However, in certain special cases the

Question:

In general, matrix multiplication is not commutative (i.e., AB ≠ BA). However, in certain special cases the commutative property does hold. Show that:
(a) If D1 and D2 are n × n diagonal matrices, then D1D2 = D2D1.
(b) If A is an n × n matrix and
B = a0I + a1A + a2A2 + ... + akAk
where ao, a1,..., ak are scalars, then AB = BA.