Unique aggregate function when singular value is guaranteed by the WHERE clause - sql

Question

Given the following:
CREATE TABLE A (A1 INTEGER, A2 INTEGER, A3 INTEGER);
INSERT INTO A(A1, A2, A3) VALUES (1, 1, 1);
INSERT INTO A(A1, A2, A3) VALUES (2, 1, 1);
I want to select the maximum A1 given specific A2 and A3 values, and have those values (A2 and A3) also appear in the returned row (e.g. so that I may use them in a join since the SELECT below is meant for a sub-query).
It would seem logical to be able to do the following, given that A2 and A3 are hardcoded in the WHERE clause:
SELECT MAX(A1) AS A1, A2, A3 FROM A WHERE A2=1 AND A3=1
However, PostgreSQL (and I suspect other RDBMs as well) balks at that and requests an aggregate function for A2 and A3 even though their value is fixed. So instead, I either have to do a:
SELECT MAX(A1) AS A1, MAX(A2), MAX(A3) FROM A WHERE A2=1 AND A3=1
or a:
SELECT MAX(A1) AS A1, 1, 1 FROM A WHERE A2=1 AND A3=1
The first alternative I don't like cause I could have used MIN instead and it would still work, whereas the second alternative doubles the number of positional parameters to provide values for when used from a programming language interface. Ideally I would have wanted a UNIQUE aggregate function which would assert that all values are equal and return that single value, or even a RANDOM aggregate function which would return one value at random (since I know from the WHERE clause that they are all equal).
Is there an idiomatic way to write the above in PostgreSQL?

Answer 1

Even simpler, you only need ORDER BY / LIMIT 1
SELECT a1, a2, a3 -- add more columns as you please
FROM a
WHERE a2 = 1 AND a3 = 1
ORDER BY 1 DESC -- 1 is just a positional reference (syntax shorthand)
LIMIT 1;
LIMIT 1 is Postgres specific syntax.
The SQL standard would be:
...
FETCH FIRST 1 ROWS ONLY
My first answer with DISTINCT ON was for the more complex case where you'd want to retrieve the maximum a1 per various combinations of (a2,a3)
Aside: I am using lower case identifiers for a reason.

Answer 2

how about group by
select
a2
,a3
,MAX(a1) as maximumVal
from a
group by a2, a3

Answer 3

Does this work for you ?
select max(A1),A2,A3 from A GROUP BY A2,A3;
EDIT
select A1,A2,A3 from A where A1=(select max(A1) from A ) limit 1

Answer 4

A standard trick to obtain the maximal row without an aggregate function is to guantee the absense of a larger value by means of a NOT EXISTS subquery. (This does not work when there are ties, but neither would the subquery with the max) When needed, it would not be too difficult to add a tie-breaker condition.
Another solution would be a subquery with a window function row_number() or rank()
SELECT *
FROM a src
WHERE NOT EXISTS ( SELECT * FROM a nx
WHERE nx.a2 = src.a2
AND nx.a3 = src.a3
AND nx.a1 > src.a1
);