Question

Give examples of matrices A and B of the same size
such that
(a) rank(A + B) < rank(A) and rank(A + B) < rank(B)
(b) rank(A + B) = rank(A) and rank(A + B) = rank(B)
(c) rank(A + B) > rank(A) and rank(A+ B) > rank(B).

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