Thanks for the response,
I refer to the routine src/mat/impls/baij/seq/dgefa6.c /* Inverts 6 by 6 matrix using gaussian elimination with partial pivoting. Used by the sparse factorization routines in src/mat/impls/baij/seq This is a combination of the Linpack routines dgefa() and dgedi() specialized for a size of 6. */ which implements the the computation of an inverse for a dense 6x6 block. I think this routine is used in the ILU numeric factorization to compute the inverse diagonal block when we later apply ILU preconditioning where we need the inverse. And there it looks we use a direct LU solve and not triangular solves ?! In this context I am not sure if something is missing at the end or not regarding the inverse pivoting ?! Greetings, Frank