My brother is . . . . . . . . Soldier. He is in . . . . . . . . army.

Answer: Option A

'The' is used as a definite article for a thing or person when the reader knows which one we are exactly referring to. It states the specific nature of the subject.
Option A is correct as 'The' is used as a definite article for a particular noun, Army in the second blank and for the first blank 'A' is used as an indefinite article for any random person when the reader doesn't know which one we are referring to out of many nouns.