Home
Class 12
MATHS
(i) Prove that (adj adj A) = |A|^(n – 2)...

(i) Prove that (adj adj A) `= |A|^(n – 2) A `
(ii) Find the value of |adj adj adj A| in terms of |A|

Text Solution

Verified by Experts

The correct Answer is:
(ii) `|A|^((n-1)^(3))`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MOTION|Exercise Exercise - 3(Comprehension - based Questions)|3 Videos

  • MATRICES

    MOTION|Exercise Exercise - 3(Matrix Match - type Questions)|1 Videos

  • MATRICES

    MOTION|Exercise Exercise - 2(Level-II) (Multiple correct Option - type Questions)|7 Videos

  • LIMIT

    MOTION|Exercise EXERCISE-4|17 Videos

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE - 4 (LEVEL - II)|17 Videos

Similar Questions

Explore conceptually related problems

Prove that : adj.O=O

Prove that : adj. I_(n)=I_(n)

adj AB -(adj B)(adj A) =

Prove that ("adj. "A)^(-1)=("adj. "A^(-1)) .

Prove that A^(-1)=(1)/(|A|)Adj(A)

If A= [{:(1,0,3),(2,1,1),(0,0,2):}] , then the value of |adj(adj A) | is

If A is a square matrix, then the value of adj A^(T)-(adj A)^(T) is equal to :

Prove that : (i) " adj " I=I (ii) " adj " O=O (iii) I^(-1)=I .

If A is a square matric of order 5 and 2A^(-1)=A^(T) , then the remainder when |"adj. (adj. (adj. A))"| is divided by 7 is

MOTION-MATRICES -Exercise - 3(Subjective - type Questions)
  1. If, E=[(0,1,0),(0,0,1),(0,0,0)]and F=[(0,0,0),(1,0,0),(0,1,0)] calcula...

    Text Solution

    |

  2. A is a square matrix of order n. l = maximum number of distinct ent...

    Text Solution

    |

  3. (i) Prove that (adj adj A) = |A|^(n – 2) A (ii) Find the value of |...

    Text Solution

    |

  4. For the matrix A=[{:(,3,2),(,1,1):}] Find a & b so that A^(2)+aA+bI=0....

    Text Solution

    |

  5. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

    Text Solution

    |

  6. If {1/2(A-A'+1)}^-1=2/lambda[(lambda-13,-lambda/3,lambda/3),(-17,10,-...

    Text Solution

    |

  7. Given A=[[2,0,-alpha],[5,alpha,0],[0,alpha,3]] For a in R-{a, b}, A^(-...

    Text Solution

    |

  8. Compute A^(-1) for the following matrix A=[(-1,2,5),(2,-3,1),(-1,1,1)...

    Text Solution

    |

  9. For the matrix A=[(4,-4,5),(-2,3,-3),(3,-3,4)] find A^(-2) .

    Text Solution

    |

  10. Gaurav purchases 3 pens, 2 bags and 1 instrument box and pays Rs. 41. ...

    Text Solution

    |

  11. Solve the following system of linear equations by using the principle ...

    Text Solution

    |

  12. Solve the following system of linear equations by using the principle ...

    Text Solution

    |

  13. By using the principle of matrix, show that the following system of eq...

    Text Solution

    |

  14. Find the number of 2xx2 matrix satisfying (i) aij is 1 or -1 (ii) ...

    Text Solution

    |

  15. If A = [[0, 1],[3,0]]and (A^(8) + A^(6) + A^(4) + A^(2) + I) V= [[0],[...

    Text Solution

    |

  16. If the matrices A=[(1,2),(3,4)] and B=[(a,b),(c,d)] (a,b,cd not all si...

    Text Solution

    |

  17. If [a b c1-a] is an idempotent matrix and f(x)=x-^2=b c=1//4 , then th...

    Text Solution

    |

  18. If the matrix A is involutary, show that (1)/(2)(I+A) and (1)/(2)(I-A)...

    Text Solution

    |

  19. A(3xx3) is a matrix such that |A|-a,R=(adj A) such that |B|=b. Find...

    Text Solution

    |

  20. Use matrix to solve the following system of equations. x+y+z=3 x+...

    Text Solution

    |