Just as William Shakespeare was the preeminent poet of England, so Robert Frost was the preeminent poet of the United States.
AS vs LIKE: When comparing- correct usage is AS+clause and LIKE+noun.
Here we are
comparing the clause (William Shakespeare was), so AS should be used and not LIKE.
Also the correct idiom is
JUST AS X . . . SO Y(A) Just as William Shakespeare was the preeminent poet of England,
so Robert Frost
Correct usage of as and idiom. So A is the correct answer.
(B)
Just like William Shakespeare was the preeminent poet of England, so Robert Frost
Uses like to compare clause so incorrect.
(C)
As William Shakespeare was the preeminent poet of England,
Robert FrostIncorrect idiomatic usage.
(D)
Just as England’s preeminent poet was William Shakespeare,
Robert FrostIncorrect idiomatic usage.
(E)
As William Shakespeare was the preeminent poet of England,
in the same manner Robert FrostIncorrect idiomatic usage.