Answer
(a, a) ∈ R$^n$ ◦ R = R$^{n+1}$ for all a ∈ A.
Work Step by Step
Use mathematical induction.
The result is trivial for n = 1.
Assume R$^n$ is reflexive.
Then (a, a) ∈ R$^n$ for all a ∈ A and (a, a) ∈ R.
Thus (a, a) ∈ R$^n$ ◦ R = R$^{n+1}$ for all a ∈ A.
