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Group theory: Show that the quaternionic group Q is a group. So my text book says...

Group theory:

Show that the quaternionic group Q is a group.

So my text book says the quaterionic group Q consists of 8 elements: 1, -1, i, -i, j, -j, k, and k. To prove that they are a group do I just run through the three axioms that prove associativity, existence of an inverse, and existence of an element? How would I do this?

Thank you.

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