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Q.Let A and B be n × n matrices such that A = A^2, B =...


Q.Let A and B be n × n matrices such that A = A^2,
B = B^2, and AB = BA = 0.
(a) Prove that rank(A + B) = rank(A) + rank(B).
(b) Prove that rank(A) + rank(In − A) = n.
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