Is it legal for employers to alter my time card and pay for breaks I did not take?

I recently began new employment as a secretary for an LLC. Three days into the job, my supervisor tells me that by law I have to be allowed to clock out 30 minutes per shift that I am working more than 7 hours. I was unaware of this and was clocked in and working for the full 8 hours my first two days of employment. On my fourth day she processed the weekly payroll and handed me my paycheck. The problem, I worked a total of 16 hours in the first two days and another 7.5 hours the third day, my check should have been calculated for a total of 23.5 hours. She only paid me for 22.5 making it clear that she deducted an hour from my time for two 30 minute breaks that I never took. Is this legal?