  Brualdi and Ma found a connection between involutions of length $n$ with $k$
descents and symmetric $k\times k$ matrices with non-negative integer entries
summing to $n$ and having no row or column of zeros. From their main theorem
they derived two alternating sums by algebraic means and asked for
combinatorial proofs. In this note we provide such demonstrations making use of
the Robinson-Schensted-Knuth correspondence between symmetric matrices and
semi-standard Young Tableau. Additionally, we restate the proof of Brualdi and
Ma's main result with this perspective which shortens the argument.
