  Given a finite-dimensional noncommutative semisimple algebra $A$ with
involution, we show that $A$ always has an RBA-basis. We look for an RBA-basis
that has integral or rational structure constants, and ask if the RBA admits a
positive degree map. For RBAs that have a positive degree map, we try to find
an RBA-basis with nonnegative structure constants to determine if there is a
generalized table algebra structure. We settle these questions for the algebras
$\mathbb{C} \oplus M_n(\mathbb{C})$, $n \ge 2$.
