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I know the converse is true, and it seems reasonable that this is true. Since the array will be of size |G|x|G|, inverses exist and are unique. There will be one row (and one column) that will represent the multiplication by the identity (since the rows and columns are permutations of the set). But I don't know about associativity; in fact I'm not even sure the if the column and row representing the identity will actually be the same element. So is there a counter-example or if it's true, a proof?