Learn Spanish (Latin America): La gorra azul es la mía.

Mía translates to mine, and it ends in -a to match the feminine noun gorra (cap). We include la to form the full possessive pronoun la mía (the one that is mine).

Can I just say La gorra azul es mía without the la before it?

Yes, you can! La gorra azul es mía simply states who owns the cap. Saying es la mía adds a little more emphasis, like saying The blue cap is the one that is mine to single it out from a group of other caps. Both are perfectly correct.

If the sentence was about a masculine noun like a car (el auto), how would this change?

Because auto is masculine, you would need the masculine pronoun el mío. The sentence would become El auto azul es el mío. Possessive pronouns always change to match the gender and number of the noun they represent.

Why does azul come after gorra?

In Spanish, descriptive words like colors generally come right after the noun they describe. So instead of blue cap, you say gorra azul (cap blue).