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Matrix differential equation in NDSolve


I would like to evaluate a matrix equation of the form:


in NDSolve where A and B are symbolic matrices. The problem is that S[t] is an unknown n x m matrix, of the same dimension as B. If I enter the first equation as shown above, Mathematica evaluates it to


that is, it assumes S[t] is a vector which is replicated to match the dimensions of B(x). How can I get Mathematica to respect the fact that S[t] is of dimension B in NDSolve. I tried holdform but this does not evaluate in NDSolve

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