Show that zero is the identity for addition on R and 1 is the identity for multiplication on R. But there is no identity element for the operations `-: RxxR->R` and `-:: R_*xxR_*->R_*dot`

Explanation

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.