Home
Class 11
MATHS
If A = [(1,0,0),(0,1,0),(a,b,-1)], show ...

If A = `[(1,0,0),(0,1,0),(a,b,-1)]`, show that `A^(2)` is a unit matrix.

Text Solution

Verified by Experts

The correct Answer is:
`A^(2)=[(1,0,0),(0,1,0),(0,0,1)] rArr` unit matrix
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 7.2|21 Videos

  • MATRICES AND DETERMINANTS

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 7.3|6 Videos

  • MATRICES AND DETERMINANTS

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE .(II CHOOSE THE CORRECT OPTION FROM THE FOLLOWING)|46 Videos

  • INTRODUCTION TO PROBABILITY THEORY

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (Choose the correct option for the following)|39 Videos

  • SETS,RELATIONS AND FUNCATIONS

    PREMIERS PUBLISHERS|Exercise II. Choose the correct option for the following. (M.C.Q)|35 Videos

Similar Questions

Explore conceptually related problems

If A=[{:(1,0,0),(1,0,1),(0,1,0):}] , then

If A= ((2,3),(-1,2)) .Show that A^(2)-4A+7I=0 whwre I is the unit matrix of order 2.

Let a and b be two real numbers such that a > 1, b > 1. If A=[(a,0), (0,b)] , then lim_(n to oo) A^(-n) is a. unit matrix b. null matrix c. 2l d. none of these

If A=[(0,1,1),(1,0,1),(1,1,0)] show that A^(-1)=1/2(A^(2)-3I) .

If A= {:[( 1,0,1),(0,1,2),(0,0,4)]:} ,then show that |3A| =27|A|

If A=[{:(0,1,1),(1,0,1),(1,1,0):}] show that A^(-1)=(1)/(2)(A^(2)=3I)

If A= [{:(0,1,1),(1,0,1),(1,1,0):}], "show that" A^(-1)=(1)/(2)(A^(2)-3I)

Let for A=[(1,0,0),(2,1,0),(3,2,1)] , there be three row matrices R_(1), R_(2) and R_(3) , satifying the relations, R_(1)A=[(1,0,0)], R_(2)A=[(2,3,0)] and R_(3)A=[(2,3,1)] . If B is square matrix of order 3 with rows R_(1), R_(2) and R_(3) in order, then The value of det. (2A^(100) B^(3)-A^(99) B^(4)) is

A= [(0,-2,1),(2,0,-4),(-1,0,0)] then A is

PREMIERS PUBLISHERS-MATRICES AND DETERMINANTS-SOLUTION TO EXERCISE 7.1
  1. Consider the matrix A(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)...

    Text Solution

    |

  2. If A = [(4,2),(-1,x)] and such that (A-2I) (A-3I) = 0, find the value ...

    Text Solution

    |

  3. If A = [(1,0,0),(0,1,0),(a,b,-1)], show that A^(2) is a unit matrix.

    Text Solution

    |

  4. If A = [(1,0,2),(0,2,1),(2,0,3)] "and" " "A^(3)-6A^(2)+7A+kI=0,find th...

    Text Solution

    |

  5. Given your own examples of matrices satisfying the conditions in each ...

    Text Solution

    |

  6. Given your own examples of matrices satisfying the conditions in each ...

    Text Solution

    |

  7. Given your own examples of matrices satisfying the conditions in each ...

    Text Solution

    |

  8. Show that f (x) f (y) = f(x+y) , where f(x)=[(cosx,-sinx,0),(sinx,co...

    Text Solution

    |

  9. If A is a square matrix such that A^(2) = A, find the value of 7A-(I+A...

    Text Solution

    |

  10. Verify the property A(B+C) = AB+AC, when the matrices A,B, and C are g...

    Text Solution

    |

  11. Find the matrix A which satisfies the matrix relation A [(1,2,3),(4,5,...

    Text Solution

    |

  12. If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)], verify the ...

    Text Solution

    |

  13. If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)], verify the ...

    Text Solution

    |

  14. If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)], verify the ...

    Text Solution

    |

  15. If A is a 3xx4 matrix and B is a matrix such that both A^(T)B and BA^(...

    Text Solution

    |

  16. Express the matrices as the sum of a symmetric matrix and a skew -sym...

    Text Solution

    |

  17. Express the matrices as the sum of a symmetric matrix and a skew -symm...

    Text Solution

    |

  18. Find the matrix A such that [(2,-1),(1,0),(-3,4)]A=[(-1,-8,10),(1,2,-5...

    Text Solution

    |

  19. If A=[(1,2,2),(2,1,-2),(x,2,y)] is a matrix such that "AA"^(T) =9I, fi...

    Text Solution

    |

  20. For what value of x, the matrix A=[(0,1,-2),(-1,0,x^(3)),(2,-3,0)] is ...

    Text Solution

    |