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(A) Given that,$a * b = 1 + ab$ $\rightarrow (1)$ For commutativity,check if $a * b = b * a$: $b * a = 1 + ba = 1 + ab = a * b$ Since $a * b = b * a$,

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commutative but not associative

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(A) Given that,$a * b = 1 + ab$ $ightarrow (1)$ For commutativity,check if $a * b = b * a$: $b * a = 1 + ba = 1 + ab = a * b$ Since $a * b = b * a$,the operation is commutative. For associativity,check if $(a * b) * c = a * (b * c)$: $(a * b) * c = (1 + ab) * c = 1 + (1 + ab)c = 1 + c + abc$ $a * (b * c) = a * (1 + bc) = 1 + a(1 + bc) = 1 + a + abc$ Since $1 + c + abc 
eq 1 + a + abc$,the operation is not associative. Therefore,the operation is commutative but not associative.

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

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