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 8

    MODERN PUBLICATION|Exercise EXERCISE|40 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise EXERCISE|40 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 9-EXERCISE
  1. Prove that [[b^2c^2, bc,b+c],[c^2a^2,ca,c+a],[a^2b^2,ab,a+b]] = 0

    Text Solution

    |

  2. Find "a" and "b" such that the function f(x)={3ax+b, if x>1 11 if x=1 ...

    Text Solution

    |

  3. If y= tan^-1 x then prove that (1+x^2) y(2) + 2xy(1) =0. Differentiate...

    Text Solution

    |

  4. Find the point (S) on the curve x=(3at)/(1+t^2), y=(3at^2)/(1+t^2) whe...

    Text Solution

    |

  5. Find the intervals in which the function y=(lnx)/(x) is increasing and...

    Text Solution

    |

  6. Evaluate int (x+1)dx/sqrt(x^2+2x-3))

    Text Solution

    |

  7. Evaluate: int(0)^(2π) dx/(1+e^sin x).

    Text Solution

    |

  8. Solve: (1+x^2)dy/dx+2xy-x^3=0

    Text Solution

    |

  9. If the sum of two unit vectors is a unit vectors find the magnitude of...

    Text Solution

    |

  10. Prove by vector method that in аny ∆ АВС. а=Ь cos С +с cos В.

    Text Solution

    |

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

    Text Solution

    |

  12. Obtain the co-ordinates of the foot of the perpendicular drawn from th...

    Text Solution

    |

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

    Text Solution

    |

  14. Prove that f:X rarr Y is injective iff for all subsets A,B of X,f(A n...

    Text Solution

    |

  15. Use matrix product [(1,-1,2),(0,2,-3),(3,-2,4)] [(-2,0,1),(9,2,-3),(6,...

    Text Solution

    |

  16. Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+...

    Text Solution

    |

  17. If A+B+C = pi, prove that [[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,c...

    Text Solution

    |

  18. Shows that the triangle of greatest area that can be inscribed in a ci...

    Text Solution

    |

  19. Evaluate the following integrals int (d theta)/(2+3cos^2theta-4sin^2 t...

    Text Solution

    |

  20. Find the equation of the straight line perpendicular to the line (x-2)...

    Text Solution

    |