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Exercise 2.8 (Solutions)

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belian? **Solutions**\\ (i) From the given table we have $0+0=0$ and $0+1=1$. This show that $0$ is ... )=(-a)+a=0$. Thus inverse of $a$ is $-a$. Hence, we conclude that set of integers form groups with re... roup. For $A\in P(S)$ where A is a subset of $S$ we have $S\in P(S)$ such that $A\cap S=S\cap A=A$. ... G$ such that $A{{A}^{-1}}={{A}^{-1}}A=I$. v) As we know for any two matrices $A,B\in G$, $AB \ne BA$