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I need help trying to solve "c dot inv(A)" after having solved for the field variable (Ax=b)

The simplyfied OpenFoam pseudo-code is:

    // create volScalarField's for governing equations
    // create volScalarField c

    fvMatrix Eqn
    (
        // governing equations - discretize
    );
    Eqn.relax();
    Eqn.solve();  // Ax=b
    
    // volScalarField phi = c & inv(A);
    // I'm at a loss on how to compute this.

x --> [1 x m] volScalarField
A --> [m x m] lduMatrix
b --> [1 x m] volScalarField --> I assume accessed with "Eqn.source();"

inv(A) = inv(L) & inv(D) & inv(U)
phi = c & ( inv(L) & inv(D) & inv(U) )

Any help on how to implement this in OpenFoam would be appreciated