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Show that there is no g in C_2 X C_2 for which 1, g, g^2, g^3...

Show that there is no g in C_2 X C_2 for which 1, g, g^2, g^3 are distinct, hence that C2 x C2 is not cyclic.

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Here we show that C2 X C2 is not cyclic that is we show that it has no generator means it has no elements taking whose power not covering all elements in that group.solution is below thank you.

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