I am trying to solve Problem 2.37, (i.e. the multivariate Robbins-Monro Algorithm). Problem 2.36 is the one-dimensional situation. I solve 2.37 in this way :
However, I found that for an invertible and symmetric matrix $A$ and a vector $b$, $AbbTA^{-1}\neq bb^T$, and hence my solution was wrong.
Can anyone help?