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6. Use the rule of inference "If A implies B, and B implies C, then A implies C." to prove the following statements: (a) If f(x) and g(x) are continuous functions on R, then lim g(f(x)) = g(ƒ(0)). x-0 (b) Let A be an n x n real matrix. If x € R" is a nonzero vector such that Ax singular (i.e. non-invertible). 0, then A² is