Banks have been tracking balances with numbers ledger books for centuries. Sure, someone could add a zero. That’s called “cooking the books” or “bank fraud”. People have been prosecuting those types of crimes for centuries as well.
Banks are subject to a large amount of audits to ensure the provenance of the money in their accounts. This also helps to build confidence among potential clients (borrowers and depositors). No one wants their bank to close up shop and disappear.
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