Briefly - there are two types of adjectives:
1. HARD (ending -ý) - mladý, starý, nový... (young, old, new)
2. SOFT (ending -í) - jarní, cizí, dnešní... (spring, strange, today´s)
ad 1. HARD adjectives - the ending is changed according to gender:
mladý muž (M), mladá žena (F), mladé obilí (N) - (young man, young woman, young corn)
nový den (M), nová zpráva (F), nové kolo (N) - (new day, new message, new bicycle)
ad 2. SOFT adjectives - the ending is the same in all genders:
cizí muž (M), cizí žena (F), cizí dítě (N) - (strange man, strange woman, strange child)
jarní den (M), jarní květina (F), jarní slunce (N) - (spring day, spring flower, spring sun).
So, "poslední láska" (the last love) - is also SOFT adjective.
Another problem is a group of POSSESIVE ADJECTIVES (I don´t wanna scare you).
poslední is an adjective with a soft ending. (Thus -í rather than -ý in the dictionary form.)
From the tips and notes at https://www.duolingo.com/skill/cs/Feminine -- "In the singular nominative form, the soft adjective endings are the same regardless of gender, -í: další muž (another man), další žena (another woman, another wife), and další dítě (another child)." (emphasis mine)
Every Czech adjective belongs to one of the two groups according to its declension: it is either so called "soft adjective" (ending with -í in the singular nominative form), or "hard adjective" (ending with -ý, -á or -é in the singular nominative form) - see the declension tables https://en.wikipedia.org/wiki/Czech_declension#Adjective .
The terms "soft" (in Czech "měkký") and "hard" ("tvrdý") are connected with the designation of the letters "i" and "y" in Czech:
"i" = "měkké i" (i.e. soft i)
"y" = "tvrdé y" (i.e. hard y) or "ypsilon"
Once they were two different sounds, but in modern Czech this is only a matter of spelling, both of these letters are pronounced the same:
"i" and "y" are pronounced [ɪ]
"í" and "ý" are pronounced [iː]
And all this relates to so called "soft, hard and ambiguous consonants/letters" - more on it here: http://www.czech-in-prague.cz/index/czech_consonants_and_vowels/0-92
It depends on what you mean by invariable... :) So called "soft adjectives" or "soft declension" (in Czech: měkká přídavná jména, měkké skloňování) always contain the "í" somewhere in the ending. One can say that the endings of soft declension are less varied than the hard declension - see the tables in this link https://en.wikipedia.org/wiki/Czech_declension#Adjective