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This question already has an answer here:

Given $A$ is a subset of grouo $G$ and $|A|>|\frac{G}{2}|$. How do i prove that each element of $G$ is product of rwo elements of $A$? I don't know where to begin, a hint would be very helpful.

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marked as duplicate by Derek Holt group-theory Jul 31 '17 at 7:40

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Hint: If $A$ is any subset of $G$, show that $g\in G$ is a product of two elements of $A$ if and only if $$ A\cap\{a^{-1}g\mid a\in A\}\neq\emptyset. $$

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