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 a0, a1, . . . , ak are scalars, then AB = BA

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 a0, a1, . . . , ak are scalars, then AB = BA