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Question: a true or false if a and b are 22...

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(a) True or False: If A and B are 2×2 matrices such that AB = 0 and A != 0, then B = 0. Give an argument valid for every such A and B if the statement is true, or give a counterexample if false.

(b) True or False: There exists a 4×3 matrix A so that the equation Ax = b is consistent for every vector b∈R^4. Justify your answer.

(c) True or False: If A is a 4×3 matrix and the equation Ax = b is consistent for a particular vector b∈R^4, then the equation Ax = cb is consistent for every scalar c. Justify your answer.

(d) True or False: If A and B are invertible 3×3 matrices and C = A^3 B^2, then C is invertible and C^-1 = (B^-1)^2 (A^-1)^3. Justify your answer.

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