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i can't immediately see a way to prove it either without assuming something about A,B
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Ok, I only hot the gist of one possible method (there are many) myself and looked up the details, but here is a hint:pic.twitter.com/qxhHvCZV40
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Yes, by tagging on zero blocks of appropriate size we can reduce to the case where A and B are square matrices.
End of conversation
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