On (\mathbb{R}), (a*b=a+\mu b). The operation will be commutative only for what value of (\mu)?

Correct answer: (1)

Step 1: Commutativity requires (a+\mu b=b+\mu a) for all (a,b). Step 2: This can be written as ((1-\mu)a=(1-\mu)b). For all (a,b), this is possible only when (\mu=1). Step 3: In parameter questions, equality must hold for all elements.