Home
Class 12
MATHS
Let A=Rxx R and be the binary operation ...

Let A=R`xx` R and be the binary operation on A defined by (a, b) *(c,d) = (a + c, b + d). Show that *is commutative and associative. Find the identity element for* on A, if any.

Promotional Banner

Topper's Solved these Questions

  • TEST PAPER 5

    MODERN PUBLICATION|Exercise PROBLEM|41 Videos

  • TEST PAPER 7

    MODERN PUBLICATION|Exercise EXERCISE|39 Videos

Similar Questions

Explore conceptually related problems

If A=N xx N and * is a binary operation on A defined by (a, b) ** (c, d)=(a+c, b+d) . Show that * is commutative and associative. Also, find identity element for * on A, if any.

Let the binary operation on Q defined as a * b = 2a + b - ab , find 3*4 .

Let A=N xx N and let* be a binary operation on A defined by (a, b) * (c,d) = (ad + bc, bd), AA (a, b), (c,d) in N xx N. Show that (i) * is commutative. (ii) * is associative. (iii) A has no identity element.

Let* be a binary operation on Q, defined by a*b= (3ab)/(5) .Show that is commutative as well as associative. Also, find its identity, if it exists.

Let * be a binary operation on Q defined by a**b=ab+1 . Determine whether * is commutative but not associative.

Let S =Q xx Q and let * be a binary operation on S defined by (a, b)* (c,d) = (ac, b+ad) for (a, b), (c,d) in S. Find the identity element in S and the invertible elements of S.

Let A=N cup {0} xx N cup {0} and Let * be a binary operation on a defined by (a, b) **(c, d)=(a+c, b+d) for (a, b), (c, d) in N. Show that. (i) B commutative as A (ii) * is associative on A

MODERN PUBLICATION-TEST PAPER 6-EXERCISE
  1. Evaluate:int (sin x-xcosx)/(x(x+sinx)) dx.

    Text Solution

    |

  2. Integrate : int sin^(-1)xdx.

    Text Solution

    |

  3. Find the particular solution of d^2 y/dx^2 =2x,given that x=0,y=2 and ...

    Text Solution

    |

  4. Solve :-(x^2+y^2)dx-2xy dy=0

    Text Solution

    |

  5. If with reference to the eight handed system of mutually perpendicular...

    Text Solution

    |

  6. If vec a =(2,3,6), vec b=(2,-2,1), vec c=(-1,0,2), find the direction ...

    Text Solution

    |

  7. Find the equation of the plane passing through (1, 3,4), (2, 1.-1) an...

    Text Solution

    |

  8. Find the equation of the plane passing through the line (x-8)/3=(y+19)...

    Text Solution

    |

  9. Find the distance of the point (-1,-5,-10) from the point of intersect...

    Text Solution

    |

  10. Let A=Rxx R and be the binary operation on A defined by (a, b) *(c,d) ...

    Text Solution

    |

  11. Let A=R-{3/5} Br f:ArarrA defined as f(x)=(3x+2)/(5x-3). Br show that ...

    Text Solution

    |

  12. Prove the following: |[ax-by-cz,ay+bx,az+cx],[bx+ay,by-cz-ax,bz+cy],...

    Text Solution

    |

  13. Find the inverse of the following matrices using elementary transforma...

    Text Solution

    |

  14. Show that the homogenous system of equations x-2y+z = 0 x+y-z = 0 ...

    Text Solution

    |

  15. (i) if x=sint, y= sinpt, then show that (1-x^2) d^2 y/dx^2 - x dy/dx +...

    Text Solution

    |

  16. A cylindrical open water tank with a circular base is to be made out o...

    Text Solution

    |

  17. Evaluate int (x^2 dx)/((x^2 +1)(x^2 +4))

    Text Solution

    |

  18. Determine the area of the region bounded by y^2=4ax by the double ordi...

    Text Solution

    |

  19. Prove by vector method that in any triangle ABC, a/sinA=b/sinB=c/sinC.

    Text Solution

    |

  20. Show that the lines (x-4)/1=(y+3)/-4=(z+1)/7 and (x-1)/2=(y+1)/-3=(z+1...

    Text Solution

    |