You work looks good: are you asking us to verify your answer?
The problem I did is below. I wasn't sure if for B=>A I was to "reverse" the way I looked at the table to do the computation or if I had to rewrite the table to have B be the first column and A be the second column. (B=>A) would then have the same truth value in each row as (A=>B).
The exercise I was suppose to do:
Construct the truth table for the compound statement (B=>A)<=>(A=>B). What
does the truth table tell you about the two statements B=>A and A=>B?
A B (A=>B) (B=>A) (B=>A)<=>(A=>B)
T T T T T
T F F T F
F T T F F
F F T T T
The truth table says that B=>A and A=>B are true only when both A and B are either True or False. In other words, when the converse is true or when A <=> B.