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Let ** be a binary operation on the set Q of rational numbers as followsa**b=a+ab. Is the binary operation commutative and associative ?

Answer»

Solution :`a**(B**C)=a**(b^2+c^2)`
`=a^2+(b^2+c^2)^2`
`(a+b)+c=(a^2+b^2)+c`
`=a^2+b^2+(c^2)^2`
`=a^2+b^2+c^4`
`THEREFORE a**(b**c)ne (a**b)**c`
`therefore **` is not associative


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