Guys, I took abstract algebra a few years back and I'm trying to refresh my memory. Heres a Q:
True or False: If (G, ∗) is a group that has two or more elements , then the binary operation ∗ is a bijection from G × G to G.
I think sometimes true. Wouldn't the identity*identity=identity? But then I'm sure there are other examples of non identity elements when multiplied equaling the same number and thus not a bijection.
Anyone think of examples?