  We show that the following semirings satisfy the same identities: the
semiring $\mathcal{R}_n$ of all reflexive binary relations on a set with $n$
elements, the semiring $\mathcal{U}_n$ of all $n\times n$ upper triangular
matrices over the boolean semiring, the semiring $\mathcal{C}_n$ of all order
preserving and extensive transformations of a chain with $n$ elements. In view
of the result of Kl\'ima and Pol\'ak, which states that $\mathcal{C}_n$ has a
finite basis of identities for all $n$, this implies that the identities of
$\mathcal{R}_n$ and $\mathcal{U}_n$ admit a finite basis as well.
