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4. (25 points). Prove the following statements. a) If A is a non-singular matrix, and & is a nonzero scalar, then KA is nonsingular and (KA) = - A K b) If a matrix, A, has a row of zeros, it is singular. c) If a matrix, A, has a column of zeros, it is singular. d) Let A and B be square matrices such that AB =0. A cannot be nonsingular unless B=0. e) Is the sum of two nonsingular matrices necessarily nonsingular? Prove your