Counterexamples in Group Theory and Linear Algebra

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I am studying Group Theory from Basic Algebra(Nathan Jacobson) and Linear Algebra by Hoffman and Kunze. The exercises in both the books are interesting. However when I try to solve question papers of grad school entrance exams, I am often confronted by Group Theory and Linear Algebra questions that require knowledge of counterexamples. I feel that the exercises from the above mentioned books do not help me much in solving such questions. Is there any book which deals with counterexamples in Algebra? I have come across such books for Analysis and Topology but not for algebra. Kindly help.

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