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First of all, E=mc^2 does not apply in all situations (depending on how you make your definitions). Second, mass is not matter. It takes much more to describe matter than its mass. Mass is a property of matter. Energy is also a property of matter.
There is no such thing as "pure energy." Fields (such as the electromagnetic one) carry energy and are usually not considered to be matter, but they once again require much more than their energy to describe them. So they cannot be called pure energy either.
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