Home
Class 12
MATHS
If A=[{:(-1,2,0),(-1,1,1),(0,1,0):}] the...

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

Text Solution

Verified by Experts

The correct Answer is:
`A^(-1)=A^2`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Textbook based MCQs|42 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Textbook Illustrations for Practice work|34 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise MISCELLANEOUS EXERCISE - 4|20 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 5 (Section-D)|4 Videos

  • INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER-7 (SECTION-D)|2 Videos

Similar Questions

Explore conceptually related problems

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

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

If A=[{:(1,2,1),(2,1,3),(1,1,0):}] then prove that A^3-2A^2-7A-4I_3=0 . Hence find A^(-1)

If A=[{:(2,3,-4),(5,1,0),(3,-2,5):}]andI=[{:(1,0,0),(0,1,0),(0,0,1):}] then show that AI=IA=A.

If A=[{:(1,0,-1),(2,1,3),(0,1,1):}] , then verify that A^(2)+A=A(A+I) where I is 3xx3 unit matrix.

If |{:(1,2,x),(1,1,1),(2,1,-1):}|=0 then find x.

If A=[{:(1,0,0),(0,1,0),(0,0,1):}] then A^(2)+2A = ……….

If A=[{:(0,1),(1,1):}]andB=[{:(0,-1),(1,0):}] show that (A+B)*(A-B)neA^(2)-B^(2) .

If A=[{:(0,-x),(x,0):}],B=[{:(0,1),(1,0):}]andx^(2)=-1 then show that (A+B)^(2)=A^(2)+B^(2) .

KUMAR PRAKASHAN-DETERMINANTS -Practice Work
  1. For the matrix A=[{:(1,2,2),(2,1,2),(2,2,1):}]. Show that A^2-4A-5I=0 ...

    Text Solution

    |

  2. If A=[{:(3,1),(7,5):}] and A^2+xI=yA then find X and Y. Hence find A^(...

    Text Solution

    |

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

    Text Solution

    |

  4. If A=[{:(1,2,1),(2,1,3),(1,1,0):}] then prove that A^3-2A^2-7A-4I3=0. ...

    Text Solution

    |

  5. If A=[{:(2,3),(1,-4):}],B=[{:(1,-20),(-1,3):}] then verify (AB)^(-1)=B...

    Text Solution

    |

  6. A=[{:(2,-3),(4,6):}] verify (adjA)^(-1)=(adjA^(-1))

    Text Solution

    |

  7. Solve system of linear equations , using matrix method if exists 3x+...

    Text Solution

    |

  8. Solve system of linear equations , using matrix method if exists 3x-...

    Text Solution

    |

  9. Solve system of linear equations , using matrix method if exists 5x-...

    Text Solution

    |

  10. Solve system of linear equations , using matrix method if exists 5x+...

    Text Solution

    |

  11. Solve system of linear equations , using matrix method if exists x-y...

    Text Solution

    |

  12. Solve system of linear equations , using matrix method if exists 3x+...

    Text Solution

    |

  13. Solve system of linear equations , using matrix method if exists 2/x...

    Text Solution

    |

  14. Solve system of linear equations , using matrix method if exists x-2...

    Text Solution

    |

  15. Solve system of linear equations , using matrix method if exists 4x-...

    Text Solution

    |

  16. Solve system of linear equations , using matrix method if exists x-y...

    Text Solution

    |

  17. The sum of three numbrs is 6. If we multiply third number by 3 and add...

    Text Solution

    |

  18. Prove that |{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}|=abc(1/a+1/b+1/c+1)

    Text Solution

    |

  19. If anebnecand |{:(a,a^3,a^4-1),(b,b^3,b^4-1),(c,c^3,c^4-1):}|=0 then p...

    Text Solution

    |

  20. Prove that |{:(sqrt(13)+sqrt3,2sqrt5,sqrt5),(sqrt(15)+sqrt(26),5,sqrt(...

    Text Solution

    |