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Show that zero is the identity for addition on R and1 is the identity for multiplication on R. But there is no identity elementfor the operations `-: RxxR->R`and `-:: R_*xxR_*->R_*dot` |
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Answer» We know that a+0=a=0+a and ` axx1 =a=1xxa AA a in R ` `implies ` 0 is the additive identity and 1 is the multiplicative identity in R. Now ,there is no element e in R such that `a-e =a=e-a AA a in R ` `:.` For `- : R xx R to R `, there is no identity element in R. Similarly, for `div : R xx R to R `, there is no identity element in R. Hence Proved. |
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