Let $*: R \times R \rightarrow R$ be defined by $a* b=a+2 b$. Then * is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) - not commutative
$a*b=a+2 b$
$(a* b)*c=a+2 b+2c$
while $a*(b*c)=a+2(b+2c)$
Not Associative as $(a* b)*c≠a*(b*c)$
$a* b=a+2b,b*a=b+2a$
$a+2b≠b+2a$ ⇒ not commutative