Question: (5) For each of the following sets with a binary operation, determine if it a group or not and explain why. If it is

(5) For each of the following sets with a binary operation, determine if it a group or not and explain why. If it is not a group, you should provide at least one of the properties which is not satisfied. (a) The set of n by n matrices with coefficients in Q under addition. (b) The set of n by n matrices with coefficients in Q under multiplication. (c) The integers with the operation a *b = 1 for any a, b Z. (d) The set of all functions from {1,2,3} to {1,2,3} under composition. (e) Z/nZ under multiplication. (f) The set {a+b3: a, b Z} CR under addition.

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