Home
Class 12
MATHS
Let M(2)(x)d={:{((x,x),(x,x)):},x inRR} ...

Let `M_(2)(x)d={:{((x,x),(x,x)):},x inRR}` be the set of `2xx2` singular matrices. Considering multiplication of matrices as a binary operation, find the identity element in `M_(2)(x)`. Also find the inverse of an element of `M_(2)`.

Text Solution

Verified by Experts

The correct Answer is:
Identity element `={:((1/2,1/2),(1/2,1/2)):}` and the inverse of an element x of `M_(2)(x)` is `{:(((1)/(4x),(1)/(4x)),((1)/(4x),(1)/(4x))):}`
Promotional Banner

Topper's Solved these Questions

  • BINARY OPERATION

    CHHAYA PUBLICATION|Exercise MCQs|5 Videos

  • BINARY OPERATION

    CHHAYA PUBLICATION|Exercise Integar Answer Type|5 Videos

  • BINARY OPERATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3 (Short Answer Type Questions)|40 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

Let M_(2)={:[(x,0),(0,y)]:},x,yinRR-{0} be the set of 2xx2 matrices, prove that the operation ** defined on M_(2) by A**B=AB,A,BinM_(2) is a binary operation.

The total number of binary operations on the set S={1,2} having 1 as the identity element is n . Find n .

A binary operation ** is defined in QQ_(0) , the set of all non-zero rational numbers, by a**b=(ab)/(3) for all a,binQQ_(0) . Find the identity element in QQ_(0) . Also find the inverse of an element x in QQ_(0) .

Let A={1,-1} be the set of square roots of unity. Considering multiplication (xx) as a binary operation on A, construct the composition table for multiplication on A. Determine the identity element for multiplication in A and the inverses of the elements.

Let M_(2) be the set of all 2xx2 singular matrices of the form {:((a,a),(a,a)):} where ainRR . On M_(2) an operation @ is defined as A@B=AB for all A,BinM_(2). Show that @ is a binary operation on M_(2) .

Let A={1,omega,omega^(2)} be the set of cube roots of unity. Prepare the composition table for multiplication (xx) on A. Show that multiplication on A is a binary operation and it is commutative on A. Find the identity element for multiplication and show that every element of A is invertible.

If M_(2) be the set of all 2xx2 matrices of the form {:((a,a),(a,a)):}, where ainR-{0} , then the identity element with respect to the multiplication of matrices as binary operation, is--

Let P(A) b the power set of non-empty set A. A binary operation ** is defined on P(A) as X**Y=XcapY for all X,YinP(A) . Detemine the identity element In P(A). Prove that A is the only invertible element in P(A).

Find the inverse of the function f(x)=(x^4+x^2+1)/x^2

IF x is real , find the maximum and minimum values of (x^2-x+1)/(x^2+x+1) also find the corresponding values of x.

CHHAYA PUBLICATION-BINARY OPERATION-EXERCISE 3 (Long Answer Type Questions)
  1. Construct the composition table for the binary operation multiplicatio...

    Text Solution

    |

  2. A binary operation ** on NN is defined by a**b=L.C.M.(a,b) for all a,...

    Text Solution

    |

  3. Let P(A) b the power set of non-empty set A. A binary operation ** is ...

    Text Solution

    |

  4. A binary operation ** is defined in QQ(0), the set of all non-zero rat...

    Text Solution

    |

  5. Let P(C ) be the power set of non-empty set C. A binary operation ** ...

    Text Solution

    |

  6. Let A=Ncup{0}xxNNcup{0}, a binary operation ** is defined on A by. (a,...

    Text Solution

    |

  7. Let A={0,1,2,3,4,5} be a given set, a binary operation @ is defined on...

    Text Solution

    |

  8. Let A=NNxxNN, a binary operation ** is defined on A by (a,b)**(c,d)=(a...

    Text Solution

    |

  9. Find the values of (i) 4+(6)2 (ii) 7+(5)7 (iii) 5+(8)2 (iv) 3xx(7)...

    Text Solution

    |

  10. Let M(2)(x)d={:{((x,x),(x,x)):},x inRR} be the set of 2xx2 singular ma...

    Text Solution

    |

  11. Prepare the composition table for addition modulo 6 (+(6)) on A={0,1,2...

    Text Solution

    |

  12. Prepare the composition table for multiplication modulo 6 (xx(6)) on A...

    Text Solution

    |

  13. A binary operaiton ^^ on the set A={1,2,3,4,5} is defined by a^^b=min(...

    Text Solution

    |

  14. Let S={1,omega,omega^(2)} be the set of cube roots of unity. Prepare t...

    Text Solution

    |

  15. Prepare the composition table for multiplication (xx) on the set of fo...

    Text Solution

    |

  16. Complete the following nultiplication table so as to define a commutat...

    Text Solution

    |

  17. A binary operation @ is defined on the set A={0,1,2,3,4,5} as follows:...

    Text Solution

    |

  18. An operation ** is defined on the set A={1,2,3,4} as follows: a**b,ab(...

    Text Solution

    |

  19. Let A={1,-1} be the set of square roots of unity. Considering multipli...

    Text Solution

    |

  20. Let ** be the binary defined on the set S={1,2,3,4,5,6} by a**b=r whe...

    Text Solution

    |