A theoretical identifiability has been derived by Shimizu et al., who prove that if $P_{X, Y}$ admits the linear model $Y := aX + N_Y$ with $X \perp \! \! \! \perp N_Y$ (model 1), then there exist $b \in \mathbb{R}$ and a random variable $N_X$ such that $X := bY + N_X$ with $Y \perp \! \! \! \perp N_X$ (model 2) if and only if $X$ and $N_Y$ are Gaussian. In other words, there is only one non-identifiable case corresponding to the linear Gaussian case. Moreover, if $X$ or $N_Y$ is non-Gaussian, when the candidate linear model with orientation X rightarrow Y holds, the candidate linear model with orientation Y rightarrow X does not hold.