Compare Lists and match data

I have two lists and both have a Loan Number and a Social Security number.
Sheet 1
Column A Column B
Loan Number Social Security Number

Sheet 2
Column A Column B
Loan Number Social Security Number

In columns C & D Sheet 1
1. Match Sheet 1 Social Security Number to Sheet 2 Social Security Number. Place the matched Social Security Number in column C if there is a match for both Social Security Number and for the Loan Number.
2. Match the Loan Number from Sheet 1 to Sheet 2 Loan Number. Place the matched Loan Number in column D if there is a match for both Social Security Number and for the Loan Number.

The challenge is to pair the two variables because there may not always be a match for both items. If there is not a match to both items the cell needs to be blank.

There might be might be many of the same loan numbers or Social Security Numbers but only one combination where both match. I only need to see where the two match,


Sheet 1
Loan Number Social Security Number
abcd 123
abcd 345
efg 123
lmn 123
opq 567

Sheet 2
Loan Number Social Security Number
aaa 789
bbb 458
abcd 345
efg 852
efg 123

Results Next to Sheet 1 if BOTH items match
Sheet 1 Sheet 2 Results
Loan Number Social Security Number Loan Number Social Security Number Loan Number Social Security Number Only if both match
abcd 123 aaa 789
abcd 345 bbb 458
efg 123 abcd 345 abcd 345 Match
lmn 123 efg 852
opq 567 efg 123 efg 123 Match

Thank you for the help, this is incredibly valuable. Take care.