That depends completely on what fare type you have booked and whether or not you’ve booked a refundable Icelandair ticket.
If you’ve purchased a basic economy Icelandair ticket, you are not permitted to cancel the ticket for a refund after the 24-hour grace period from when your ticket was booked.
Note: The 24-hour grace period as per The Airlines Reporting Corporation (ARC). When you book tickets from the United states.
If you have a non-refundable Icelandair ticket you will be required to pay a few bucks domestic tickets and international ticket fees range from $200 to $500 (depending on the length of the flight. Afterward, you will receive the remainder of your fare, minus the fee, in the form of an e-Credit for use on a future Icelandair flight.
If you have a Icelandair refundable or flex ticket you can cancel anytime before the departure of your flight and you will be reimbursed on your original method of payment.