I hear this sentence very often, for example:
"I am right, aren't I!"
I wonder if that is the colloquial way or it is a correct English.
I hear this type of sentence very often, for example:
- "I am right, aren't I?"
I wonder if that is the colloquial way, or if it is correct English.
Well, let's see what the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language (CGEL), says about this topic. On page 1612 is this:
The negative of am
The regular negative form %amn't is restricted to certain dialects, notably of Scotland and Ireland. In interrogatives with subject-auxiliary inversion / . . . / is widely used: Aren't I going to be invited?; I'm right, aren't I? The earlier spellings a'n't and an't have given way to aren't, reflecting its homophony with the negative of are. Aren't I is fully established in BrE or AmE, though in informal AmE ain't I would often be substituted.
However, in uninverted constructions *I aren't is not admissible even in informal style. Those who have ain't, use that here, while others use analytic negation: I am not or I'm not.
is almost identical to an example that the 2002 CGEL used in that excerpt: "I'm right, aren't I?"
And so, your example would be considered to be standard English (w.r.t. the authors of the 2002 CGEL). Or, perhaps, using your terminology: it is "correct English".
(Aside: on page 75 in the 2002 CGEL, the verb form "aren't" is shown in  as a negative present-tense verb form for the BE verb lexeme, for the 1st person singular and all others except for 3rd person singular.)
It's kind of a contested issue, because some people are pedants, and insist that "aren't" must be a contraction of "are not," and thus cannot be used where one would technically need to say "am not."
That said, this is perfectly fine colloquial English and would be acceptable in all but the most formal contexts in the US. It is used frequently in business English. In fact, the alternative "am I not?" would seem inappropriately formal in almost all settings--I only ever see it used either humorously (being playfully over-formal) or to express exasperation/frustration (by reverting to a very formal register).