Home
Class 12
MATHS
If A=[(4,-1,-4 ),(3, 0,-4),( 3,-1,-3)] ,...

If `A=[(4,-1,-4 ),(3, 0,-4),( 3,-1,-3)]` , show that `A^2=I_3`

Text Solution

Verified by Experts

Given that,
`A=[(4,-1,-4 ),(3, 0,-4),( 3,-1,-3)]`
`A^2=A*A`
`=[(4,-1,-4 ),(3, 0,-4),( 3,-1,-3)][(4,-1,-4 ),(3, 0,-4),( 3,-1,-3)]`
`=[(16-3-12,-4+0+4,-16+4+12),(12+0-12,-3+0+4,-12+0+12),(12-3-9,-3+0+3,-12+4+9)]`
`=[(1,0,0),(0,1,0),(0,0,1)]`
`=I_3`
`therefore A^2=I_3`
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA|Exercise Solved Examples And Exercises|331 Videos

Similar Questions

Explore conceptually related problems

(i) if A=[{:(4,-1,-4),(3,0,-4),(3,-1,-3):}], then show that A^(2)=I

If A=|{:(4,-1,-4),(3,0,-4),(3,-1,-3):}| , then show that A=A^(-1)

If A=[{:(2,-2,-4),(-1," "3," "4),(1,-2,-3):}], show that A^(2)=A.

If A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}] , then show that A^(3)=A^(-1) .

If A=[(3,-3,4),(2,-3,4),(0,-1,1)]2-3 41 then show that A^-1=A^1.

If A=[(3,-3,4),(2,-3,4),(0,-1,1)] , then :

If A=[(1, 2, 0 ),(3,-4, 5),( 0,-1, 3)] , compute A^2-4A+3I_3 .

If A=[(3,-3,4),(2,-3,4),(0,-1,1)] , then A^(-1)=

If A+I={:[(2,2,3),(3,-1,1),(4,2,2)]:} then show that A^(3)-23A-40I=0

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If omega is a complex cube root of unity, show that ([(1,omega,omega...

    Text Solution

    |

  2. If A=[(2,-3,-5),(-1 ,4 ,5),( 1,-3,-4)] , show that A^2=A .

    Text Solution

    |

  3. If A=[(4,-1,-4 ),(3, 0,-4),( 3,-1,-3)] , show that A^2=I3

    Text Solution

    |

  4. If [1\ \ 1\ \ x][1 0 2 0 2 1 2 1 0][1 1 1]=0 , find xdot

    Text Solution

    |

  5. If [(2,3),(5,7)][(1,-3),(-2,4)]=[(-4,6),(-9,x)] , find xdot

    Text Solution

    |

  6. If [(x,4,1)][(2,1,2),(1,0,2),(0,2,-4)][(x),(4),(-1)]=0 , find xdot

    Text Solution

    |

  7. If [(1, -1,x)][(0 ,1,-1),( 2 ,1 ,3),( 1 ,1 ,1)][(0),( 1),( 1)]=0 , fin...

    Text Solution

    |

  8. If A=[(3,-2),( 4,-2)] and I=[(1 ,0),( 0 ,1)] , then prove that A^2-A+2...

    Text Solution

    |

  9. If A=[(3 ,1),(-1, 2)] and I=[(1, 0), (0 ,1)] , then find lambda so tha...

    Text Solution

    |

  10. If A=[[3 ,1],[-1, 2]] , show that A^2-5A+7I2=O .

    Text Solution

    |

  11. If A=[(2, 3),(-1 ,0)] , show that A^2-2A+3I2=O .

    Text Solution

    |

  12. Show that the matrix A=[(2, 3), (1, 2)] satisfies the equation A^3-4A...

    Text Solution

    |

  13. Show that the matrix A=[(5, 3), (12 ,7)] is a root of the equation A...

    Text Solution

    |

  14. If A=[(3,-5),(-4, 2)] , find A^2-5A-14 Idot

    Text Solution

    |

  15. If A=[(3, 1),(-1, 2)] , show that A^2-5A+7I=O . Use this to find A^4

    Text Solution

    |

  16. If A=[(3,-2) ,(4,-2)] , find k such that A^2-k A-2I2=0 .

    Text Solution

    |

  17. If A=[(1, 0),(-1 ,7)] , find k such that A^2-8A+k I=O .

    Text Solution

    |

  18. If A=[(1 ,2 ),(2, 1)] and f(x)=x^2-2x-3 , show that f(A)=O .

    Text Solution

    |

  19. If A=[(2, 3),( 1, 2)] and I=[(1, 0),( 0, 1)] , then find lambda,mu ...

    Text Solution

    |

  20. Find the value of x for which the matrix product [(2, 0, 7),( 0, ...

    Text Solution

    |