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Question Number 191937 by Mastermind last updated on 04/May/23

$$\mathrm{Check}\mathrm{whether}(\mathrm{Q},\cdot )\mathrm{is}\mathrm{a}\mathrm{group}\mathrm{or}$$$$\mathrm{not}$$$$$$$$\mathrm{Hello}\mathrm{bosses}!$$

Answered by deleteduser1 last updated on 04/May/23

$$Leta,b\in Q(Q=\frac{x}{y})wherea=\frac{x_1}{y_1},b=\frac{x_2}{y_2}$$$$a\cdot e=e.a=a$$$$\Rightarrow e=a\cdot a^{-1}=1$$$$whereaunique{a}^{-1}\in Q$$$$Theredoesnotexistaunique{a}^{-1}\in Qfora=0$$$$suchthata\cdot a^{-1}=1.Hence,Qcannotbeagroup.$$

Commented by Mastermind last updated on 04/May/23

$$\mathrm{Thak}\mathrm{you}\mathrm{BOSS},\mathrm{i}\mathrm{do}\mathrm{really}\mathrm{appreciate}$$

Commented by Mastermind last updated on 04/May/23

$$200\mathrm{l}$$

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