Prove or find a counterexample to disprove each of the following: (a) rank(A + B) ( max{rank

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Prove or find a counterexample to disprove each of the following:
(a) rank(A + B) ( max{rank A, rank B}
(b) rank(A + B) ( min{rank A, rank B}
(c) rank(A + B) = rank A + rank B
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