#12. Let A be an m × n matrix and B be an n × p matrix. Prove that (a) N(B) C N(AB). (b) C(AB) C C(A). (Hint: Use Proposition 4.1.) (c) N(B) = N(AB) when A is n x n and nonsingular.

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A: A=12-3012143

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A: Given C = A - 2B

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A: I am going to solve the given problem by using some simple calculus to get the required result.

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