Is “A -> aAA” convertible to regular grammar?
You can prove inductively that any word $w$ generated by your grammar satisfies $$\#_b(w) + \#_c(w) = \#_a(w) + 1.$$
Also, you can prove inductively that for every $n$, your grammar generates a word having $a^n$ as a prefix.
You can now use the pumping lemma to show that the language generated by your grammar isn't regular.
Variant: intersect the language generated by your grammar with $a^*b^*$ to get an explicit language which is not regular.