We use the notation F to denote either the field R of real numbers or the field C of complex numbers. This problem reviews what a field is. (See Ch. 1.) Determine whether the following sets (with the usual senses of multiplication, addition, etc.) are fields or not. If the answer is Yes then you may say so without proof. If the answer is No then give a concrete counterexample for one of the defining properties of a field that is violated. (a) The set of numbers that are irrational or zero, i.e., the set (R Q) {0} (b) The set of N N diagonal matrices (where the "1" element is IN , and the "0" element is 0N N ). (c) The set of N N diagonal matrices whose diagonal elements are either all zero or all non-zero. (d) The set of rational functions, i.e., functions of the form P(x)/Q(x) where P and Q are both polynomials and Q is not zero. (e) The set of N N invertible matrices along with the N N zero matrix