  We give a short and elementary proof of the fact that for a linear
complementary pair $(C,D)$, where $C$ and $D$ are $2$-sided ideals in a group
algebra, $D$ is uniquely determined by $C$ and the dual code $D^\perp$ is
permutation equivalent to $C$. This includes earlier results of Carlet et al.
and G\"uneri et al. on nD cyclic codes which have been proved by subtle and
lengthy calculations in the space of polynomials.
