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Can two companies own stock in each other?
Absolutely. In fact, all stock purchases of more than 5% of a company's stock must be reported to the SEC, so assuming A and B are publicly traded companies in the US, the purchase would likely be a matter of public record.  There are probably special cases where this could cause problems, however; any case where A's purchase of B's stock (or vice versa) runs afoul of regulation would be one such case. For example, if company A wants to own a controlling interest in company B and appoint members of its board of directors and both companies were in the same heavily-concentrated market, regulators may frown on the potential for decreased competition. Such regulations may apply to any purchase of a controlling interest in a company, though.