This paper shows that for the Euler-Maruyama method applied to a stochastic differential equation (SDE), it possesses a modified Kolmogorov operator that can be expanded in powers of the stepsize. In the case the SDE is elliptic or hypoelliptic, a weak backward error analysis result holds. This implies that every invariant measure of the method is close to a modified invariant measure obtained by asymptotic expansion, and that the method is exponentially mixing up to some very small error and for all times.