Conditional density calculation

Question

If we know the density of a vector $x$ is $f(x)$, which could be multivariate standard normal $N(0,I_r)$, and we know the conditional density of $f(y|x)$, which is multivariate normal $N(Ax,I_T)$ with $A$ being a $A \times r$ matrix with $T>r$. My question is how to derive the conditional density $f(x|y)$. Any suggestions or reference? Thanks