The principle of double entry system ensures mathematical accuracy in trial balance. This principle states that for every transaction, there are at least two accounts affected: a debit account and a credit account. The debit and credit amounts for each transaction must be equal in value, ensuring that the total debits and total credits always balance. This ensures that errors in recording transactions can be easily detected and corrected by checking the mathematical accuracy of the trial balance, which lists all the debit and credit balances in the ledger accounts.