For any two real numbers, an operation * defined by $a * b = 1+ ab$ is

The correct answer is commutative but not associative

Given that $a * b = 1+ ab$


Now, $b * a = 1+ ba = 1 + ab = a*b$

⇒ $a*b = b*a$

This $*$ is commutative.


Now, $(a*b)*c = (1 + ab)*c$

= $1 + (1 + ab)c$

= $1 + c + abc$

$a*(b*c) = a*(1 + bc)$

= $1 + a(1 + bc)$

= $1 + a + abc$


So, $(a*b)*c \ne a*(b*c)$

Thus $*$ is not associative.

Hence $*$ is commutative but not associative