Let * be a binary operation on `R` defined by `a*b=a b+1` . Then, * is commutative but not associative associative but not commutative neither commutative nor associative (d) both commutative and associative

Answer

N/a

Explanation

(i) Given that, `a**b=1+ab, AA a,b in R`
`a**b=ab+1=b*a`
So, `**` is a commutative binary operation.
Also, `a**(b**c)= a**(1+bc)=1+a(1+bc)`
`a**(b**c)=1+a+abc " " ` …(i)
` (a**b)**c=(1+ab)**c`
`=1+(1+ab)c=1+c+abc " " `...(ii)
From Eqs. (i) and (ii),
`a**(b**c) ne (a**b)**c`
So, `** ` is not associative
Hence, `**` is commutative but not associative.