How to retrieve rows with max value in one column for each combination of other two columns?

Question

I need to query an SQL database to find all records with max RATE for each combination of fields A and B. For example, consider the following table with 4 columns, A, B, RATE & VALUE:

A B RATE VALUE
= = ==== =====
a b 10   100
a b 2    110
a c 1    20
a c 3    55
a d 8    22
b c 3    10

I wish to get back one row from each distinct pair A & B with max RATE, getting these rows:

A B RATE VALUE
= = ==== =====
a b 10   100
a c 3    55
a d 8    22
b c 3    10

How can I formulate such a query in SQL?