Let $D_3$ be the Dickson invariant algebra of $F_2[X_1,; X_2,; X_3] ; by ; GL(3,; F_2)$. In this paper, we provide an elementary proof of Theorem 3.2 of [2]; each element in $D_3$ is hit by the Steenrod square in $F_2[X_1,; X_2,; X_3]$