I am trying to find the solution of Exponential Mixture density, which is to estimate covariance and mean of a new Gaussian distribution from data fusion of several Gaussian distributions. Suppose I have A, B and a, b, which are covariance and mean of two Gaussian. The new covariance C and mean c is given by:

C=inv(omig1*inv(A)+omig2*inv(B))

c=C(omig1*inv(A)*a+omig2*inv(B)*b)
minimize （D1-D2）^2
s.t. omig1+omig2=1
Where D1 and D2 is KL divergence.
Since inv cannot be used, I just omig1*inv(A) into omig1/A.However this doesn’t work for C:

C=1/(omig1/A+omig2/B)

It says divider matrix must be constant.So how can I generate inverse matrix over here.