3. Let A, B,C be n x n matrices. (a) Show that rank(AB) = rank(B) if...

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3. Let A, B,C be n x n matrices. (a) Show that rank(AB) = rank(B) if and only if the systems (AB)x 0 and Bx 0 have the same solutions. (b) If rank(AB) = rank(B), show that rank(ABC) = rank(BC). 3. Let A, B,C be n x n matrices. (a) Show that rank(AB) = rank(B) if and only if the systems (AB)x 0 and Bx 0 have the same solutions. (b) If rank(AB) = rank(B), show that rank(ABC) = rank(BC).