Make a truth table to prove this: $(a \rightarrow b) \Leftrightarrow (\bar{b} \rightarrow \bar{a})$

Question

I hope my table is correct because I know that this is true but I have troubles in designing the table. I did it like this and I'd like to know if it's good?

"-" stands for "NOT"

a    b    a→b    -a    -b     -b → -a
--------------------------------------
0    0     1      1     1        1
0    1     1      1     0        1
1    0     0      0     1        0
1    1     1      0     0        1

But if I look at my table it seems contradicting because the results are different...