NO, the Executive Committee cannot prevent you from inspecting any of your Owners Corporation’s records, and you can apply in writing to inspect those under the provisions of Sect 108 of the NSW Strata Schemes Management Act (1996); the currently prescribed fee payable to the Owners Corporation is $31 for the first hour that the records are being made available and an additional $15 for each half-hour thereafter, plus any administrative fees disbursements that your Strata Manager may themselves charge for printing etc.
Even though it sounds as though your Executive Committee does not wish to make those records available to you, and that’s understandable given your last post regarding its Secretary paying herself for cleaning duties, it would still be advisable in my opinion for you to advise (with your application) precisely what record/s you wish to inspect with the expectation that your Strata Manager (S/M) will have those ready, as opposed to just dumping you with the lot and thereby forcing you to trawl through everything.
Good luck!