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Question Number 119684 by help last updated on 26/Oct/20

Commented by help last updated on 26/Oct/20

$$istheoperationclosed$$

Commented by help last updated on 26/Oct/20

$$isitcommutative$$$$isitassociative$$$$identityoftheelements$$$$inverseofi$$$$inverseof-1$$

Answered by $@y@m last updated on 26/Oct/20

$$LetS=\{-1,1,i,-i\}$$$$Fromoperationtable,$$$$\left(i\right)a\ast b\in S\mathrm{\forall }a,b\in S$$$$\therefore \ast isclosed.$$$$\left(ii\right)a\ast b\in b\ast a\mathrm{\forall }a,b\in S$$$$\therefore \ast iscommutative.$$$$\left(iii\right)Tryyourself.$$$$\left(iv\right)a\ast 1=a\mathrm{\forall }a\in S$$$$\therefore 1istheunityelement.$$$$\left(iv\right)i\ast (-i)=1$$$$\therefore -i\in Sisinverseofi$$$$\left(v\right)Tryyourself$$

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