Can the AAR & AAAR order for rectification of mistakes in the ruling?

Yes. Section 101 of the Act gives power to AAR
and AAAR to amend their order to rectify any mistake
apparent from the record within a period of six months
from the date of the order. Such mistake may be noticed
by the authority on its own accord or may be brought
to its notice by the applicant or the prescribed or the
jurisdictional CGST/SGST officer. If a rectification has
the effect of enhancing the tax liability or reducing the
quantum of input tax credit, the applicant must be heard
before the order is passed.