Home
Class 12
MATHS
Prove that the operaton ** on QQ-{1} giv...

Prove that the operaton `**` on `QQ-{1}` given by `a*b=a+b-ab` for all `a,binQQ-{1}`
(i) is closed:
(ii) satisfies the commutative and associative laws,
(iii) Find the identity element,
(iv) Find the inverse of any element `ainQQ-{1}.`

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

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.

A binary operation ** on NN is defined by a**b=L.C.M.(a,b) for all a,binNN . (i) Find 15**18 (ii) Show that ** is commutative as well as associative on NN. (iii) Find the the identity element in NN . (iv) Also find the invertible element in NN .

A binary @ on NN is defined by a@b=L.C.M.(a,b) for all a,binNN. (i) Examine the commutativity and associativity of @ on NN , (ii) Find the identity element in NN , (iii) Also find the invertible elements of NN .

A binary operation @ is defined on RR-{-1} by a@b=a+b+ab for all a,binRR-{-1}. (i) Discuss the commutativity and associativity of @ on RR-{-1} . Find the identity element, if exists. (iii) Prove that every element of RR-{-1} is invertible.

Prove that the binary operation @ defined on QQ by a@b=a-b+ab for all a,b in QQ is neither commutative nor associative.

An operation @ on QQ-{-1} is defined by a@b=a+b+ab for a,binQQ-{-1}. Find the identity element einQQ-{-1} .

A binary operation @ on QQ-{1} is defined by a**b=a+b-ab for all a,binQQ-{1}. Prove that every element of QQ-{1} is invertible.

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.

Discuss the commutativity and associativity ** on QQ defined by a**b=ab+4 for all a,binQQ.

Let ** be a binary operation on set QQ-{1} defined by a**b=a+b-abinQQ-{1}. e is the identity element with respect to ** on QQ . Every element of QQ-{1} is invertible, then value of e and inverse of an element a are---