Home
Class 12
MATHS
Show that the operation ** defined on R...

Show that the operation `**` defined on `RR-{0}` by `a**b=|ab|` is a binary operation. Show also that `**` is commutative and associative.

Promotional Banner

Topper's Solved these Questions

  • BINARY OPERATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3(MCQs)|9 Videos
  • BINARY OPERATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3(Very Short Answer Type Questions)|22 Videos
  • ARCHIVE

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive|13 Videos
  • BINOMIAL DISTRUTION

    CHHAYA PUBLICATION|Exercise ASSERTION-REASON TYPE|2 Videos

Similar Questions

Explore conceptually related problems

Prove that the operation ** on ZZ defined by a**b=a|b| for all a,binZZ is a binary operation

Show that the binary operation ** defined on RR by a**b=ab+2 is commutative but not associative.

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

Let * be a binary operation defined by a* b = L.C.M , (a,b) AA a,b in N . Show that the binary operation * defined on N is commutative and associative. Also find its identity element of N.

The binary operation * define on N by a*b = a+b+ab for all a,binN is

Let A = N xx N and ** be the binary opertion on A defined by (a,b) ** (c,d) = (a + c, b+d) Show that ** is commutative and associative.

Show that the operation ** on ZZ , the set of integers, defined by. a**b=a+b-2 for all a,b inZZ (i) is a binary operation: (ii) satisfies commutaitve and associative laws: (iii) Find the identity elemetn in ZZ , (iv) Also find the inverse of an element ainZZ.

Let RR be the set of real numbers. Show that the operation ** defined on RR-{0] by a**b=|ab|,a,binRR-{0} is a binary operation on RR-{0}.

Let A=Ncup{0}xxNNcup{0}, a binary operation ** is defined on A by. (a,b)**(c,d)=(a+c,b+d) for all (a,b),(c,d)inA. Prove that ** is commutative as well as associative on A. Show also that (0,0) is the identity element In A.

let ** be a binary on QQ , defined by a**b=(a-b)^(2) for all a,binQQ . Show that the binary operation ** on QQ is commutative but not associative.