Can my mother get Medicare and Medicaid at the same time?

Yes, people who receive both Medicare and Medicaid are called "Dual Eligibles." The federal government has information online about the programs here:
https://www.cms.gov/apps/firststep/content/medicare_dualelig.html

Thanks, Gabriel. This is important information.
Carol

My dad is already receiving both medicare and medicaid in Illinois. If I move him to California would he still be covered or would we have to reapply?

my mother receives a ss ck for 978.00 after they take out 104.00 for medicare she also has tri-care for life through my late dad she is also eligible for Medicaid?