Is the double-entry accounting transaction always equal?

Yes. In double entry accounting every number is entered twice. There are two columns, debits and credits. Every dollar is debited against one account and credited to another account. This makes it easier to keep track of where the money is going. Then when an accountant checks the company books against the cash on hand and against the bank accounts it makes it real easy to find out if fraud is occurring. A problem comes when a company uses the same accountant year after year and the person stealing the money bribes the accountant not to report the fraud. Then the system does not work.