> It's not. You want to know the most probable value of A.

Nah, it's really not that simple. When I've done this in the past, I've needed both the mean (which is the mode for Normal distributions) and the variance, so I can make confidence ellipses. I don't just care about the most probable location.

I already have a set of techniques for working with Kalman filters. The only reason I would want to understand applying the Bayes' theorem in this context is if it offers insight into a wider class of problems (non-Gaussian PDFs) or if it helps me communicate with others. In both of those cases, I'd like to understand the thing first before I hand-waive the denominator away.