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Question Number 187186 by 073 last updated on 14/Feb/23

Commented by 073 last updated on 14/Feb/23

$$\mathrm{please}\mathrm{solution}??$$

Commented by Rasheed.Sindhi last updated on 15/Feb/23

$$\mathrm{k}=4\left(\mathrm{please}\mathrm{confirm}\mathrm{the}\mathrm{answer}\right)$$

Commented by mr W last updated on 15/Feb/23

$$k=4iscorrect.$$

Commented by Rasheed.Sindhi last updated on 16/Feb/23

$$\mathit{s}\mathit{i}\mathit{r}mrW,whenyouhavesomeleisure$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$foritshealth!$$

Commented by 073 last updated on 16/Feb/23

$$\mathrm{thanks}$$

Commented by 073 last updated on 16/Feb/23

$$\mathrm{thanks}$$

Answered by Rasheed.Sindhi last updated on 15/Feb/23

$$\overline{)\begin{array}{cccccc}★& 1& 2& 3& 4& 5\\ 1& 5& 1& 2& 3& 4\\ 2& 1& 2& 3& 4& 5\\ 3& 2& 3& 4& 5& 1\\ 4& 3& 4& 5& 1& 2\\ 5& 4& 5& 1& 2& 3\end{array}}$$$$\mathrm{A}=\{1,2,3,4,5\}$$$$\mathrm{x}★\mathrm{e}=\mathrm{x}\mathrm{\forall }\mathrm{x}\in \mathrm{A}\Rightarrow \mathrm{e}=2$$$$1^{-1}=3[\because 1★3=2]$$$$2^{-1}=2[\because 2★2=2]$$$$3^{-1}=1[\because 3★1=2]$$$$4^{-1}=5[\because 4★5=2]$$$$5^{-1}=4[\because 5★4=2]$$$$$$$${\left(2★\mathrm{k}\right)}^{-1}★5=3$$$${\mathrm{k}}^{-1}★5=3[\because 2★\mathrm{k}=\mathrm{k}]$$$${\mathrm{k}}^{-1}★5★5^{-1}=3★5^{-1}$$$${\mathrm{k}}^{-1}★\left(5★5^{-1}\right)=3★4[\because 5^{-1}=4]$$$${\mathrm{k}}^{-1}★2=3★4[\because 5★5^{-1}=2]$$$${\mathrm{k}}^{-1}=5[\because {\mathrm{k}}^{-1}★2={\mathrm{k}}^{-1}]$$$$\mathrm{k}=4$$

Commented by 073 last updated on 16/Feb/23

$$\mathrm{thanks}\mathrm{alot}\mathrm{sir}$$

Answered by mr W last updated on 15/Feb/23

$$x\ast e=x\Rightarrow e=2$$$$x\ast x^{-1}=e=2\Rightarrow 1^{-1}=3,2^{-1}=2,3^{-1}=1,4^{-1}=5,5^{-1}=4$$$$5\ast 5=3\Rightarrow {(2\ast k)}^{-1}=5\Rightarrow 2\ast k=4\Rightarrow k=4✓$$

Commented by 073 last updated on 16/Feb/23

$$\mathrm{nice}\mathrm{solution}$$

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