#asymmetry

The KL divergence is not symmetric in general. True or false: for two Gaussians with the same variance, $P = \mathcal{N}(\mu_1, \sigma^2)$ and $Q = \mathcal{N}(\mu_2, \sigma^2)$, the two directions agree, $D_{\mathrm{KL}}(P \| Q) = D_{\mathrm{KL}}(Q \| P)$.