When can an adjective be postposed?

Solution 1:

Question 1: They both sound good to me, but I prefer "military matters" because it's not pretentious or excessively literary. Question 2: There are a few adjectives, e.g., galore, that must be postposed.

There are sentences in which postposing the adjective is normal:

In some instances, adjectives can follow the direct object, in which case it is described as postposed, such as
'he paints the house red',
'they made the party wonderful'.

There are set phrases with postposed adjectives:

court-martial
attorney general

Solution 2:

We all know the rule of thumb that you ‘never put an adjective after the noun which it is describing’.

A more accurate statement is: Adjectives usually occur in the attributive or the predicative position; there are some that are used solely, or in certain circumstances, post-positively (adjectives do as well appear in reduced clauses and sentence fragments).

Collins CoBuild English Grammar lists four sub-classes of post-positive adjectives, ie adjectives which must or may be used post-nominally (Points 1 - 4 below are taken from my copy of Collins CoBuild English Grammar, though I've added the comments for class 1 and given new examples. The rest, apart from the obvious reference back to the thread, is semi-original - I can't remember where I've picked it up or my selection process for retaining as valuable / discarding. I'm certainly quoting myself in part from 'Wordwizard'. Oh, and the fourth position for adjectives is the absolute usage: Happy with his lolly, Tim did not see the kingfisher dart past.):

1. Adjectives used only post-positively: designate elect extraordinaire incarnate manqué (galore is often included here, but I think is far more quantifier-ish) (note the loan-word connection involved; in French, adjectives are usually postposed, of course)

2. Some adjectives are used immediately after a measure, eg three miles high: broad deep high long old tall thick wide

3. The adjectives concerned involved present responsible proper can be used before or after the noun they modify – but the meaning changes: Do you think they are responsible people? The people responsible will be brought to justice.

4. The adjectives affected available required suggested may be used either pre- or post-nominally with no change of meaning: We haven’t got the required money / money required.

I’d add a fifth usage - deliberately archaizing contexts (regards to StoneyB), often with a nod to G & S say. matters military; matters mathematical where the accepted word order is reversed for effect. This could get very tedious very quickly, and prompted the original posting.

Attributive adjective + noun (phrase) and noun (phrase) + post-positive adjective have often become collocations or even compound nouns (red sunset; Blue Moon // devil incarnate; President Elect), and are often set idioms.

I'd suggest that especially Latin connections are jealously guarded by highbrow scholars (as in present continuous) and lawyers (as in fee simple absolute), in their jargon.