Yes, if you enroll when eligible.
However, it can get even a bit more complicated if you enroll in Medicare after 65.
In that case, the coverage can be back-dated up to six months depending on when you were eligible for coverage.
So if you apply at 65.5, the coverage will be backdated to the month you turned 65.
If you apply at 70, the coverage will be 6 months prior to that date.
If you apply at 65 and 3 months, the coverage would be back-dated three months.
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