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Let A=RR(0)xxRR where RR(0) denote the s...

Let `A=RR_(0)xxRR` where `RR_(0)` denote the set of all non-zero real numbers. A binary operation `**` is defined on A as follows: `(a,b)**(c,d)=(ac,bc+d)` for all `(a,b),(c,d)inRR_(0)xxRR.`
Binary operation `**` is--

A

commutative but not associative A

B

commutative and associative on A

C

associative but not commutative on A

D

none of these

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • Let A=RR_(0)xxRR where RR_(0) denote the set of all non-zero real numbers. A binary operation ** is defined on A as follows: (a,b)**(c,d)=(ac,bc+d) for all (a,b),(c,d)inRR_(0)xxRR. The inveritible elements in A is---

    A
    `(-(1)/(b),-(b)/(a))`
    B
    `(-(1)/(b),(b)/(a))`
    C
    `((1)/(b),(b)/(a))`
    D
    `((1)/(a),-(b)/(a))`

  • QQ^(+) denote the set of all positive raional numbers. If the binary operation @ on QQ^(+) is defined as a@b=(ab)/(2) , then the inverse of 3 is---

    A
    `(4)/(3)`
    B
    2
    C
    `(1)/(3)`
    D
    `(2)/(3)`

  • The binary operation ** defined on NN by a**b=a+b+ab for all a,binNN is--

    A
    commutaitive only
    B
    associative only
    C
    commutative and associative both
    D
    none of these

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