Home
Class 12
MATHS
If A is a square matrix such that A(adjA...

If `A` is a square matrix such that `A(adjA)=[(4,0,0),(0,4,0),(0,0,4)],` then `=(|adj(adjA)|)/(2|adjA|)` is equal to

Text Solution

Verified by Experts

We know that A (adj. A) `=|A|I_(n)`
`:. |A|=4`
(i) `|"adj. "A|=|A|^(2)=4^(2)=16`
(ii) `|"adj. (adj. A)"|=|A|^((n-1)^(2))=4^(4)=256" "( :' n=3)`
(iii) `|"adj. (3A)"|=|3^(3-1)" (adj. A)"|=(3^(2))^(3)|"adj. A"|=3^(6)xx16`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise 13.1|5 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.2|6 Videos

  • MATRICES

    CENGAGE|Exercise Multiple Correct Answer|7 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

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

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

Let A be a square matrix of order 3 such that adj. (adj. (adj. A)) =[(16,0,-24),(0,4,0),(0,12,4)] . Then find (i) |A| (ii) adj. A

If A is a square matrix of order 3 such that |A|=5 , then |Adj(4A)|=

The matrix is [(4,3,1),(0,2,3),(0,0,-2)] is:

For any 2xx2 matrix if A (adj A )= [(10,0),(0,10)] then find |A|.

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

CENGAGE-MATRICES-Examples
  1. Find the adjoint of the matrix A=[(1,1,1),(2,1,-3),(-1,2,3)].

    Text Solution

    |

  2. If S=[((sqrt(3)-1)/(2sqrt(2)),(sqrt(3)+1)/(2sqrt(2))),(-((sqrt(3)+1)/(...

    Text Solution

    |

  3. If A is a square matrix such that A(adjA)=[(4,0,0),(0,4,0),(0,0,4)], t...

    Text Solution

    |

  4. Let A be a square matrix of order 3 such that adj. (adj. (adj. A)) =...

    Text Solution

    |

  5. Let A =[(1,-1,1),(2,1,-3),(1,1,1)] and 10B=[(4,2,2),(-5,0,alpha),(...

    Text Solution

    |

  6. Matrices a and B satisfy AB=B^(-1), where B=[(2,-1),(2,0)]. Find (i...

    Text Solution

    |

  7. Given the matrices a and B as A=[(1,-1),(4,-1)] and B=[(1,-1),(2,-2)]....

    Text Solution

    |

  8. If M is the matrix [(1,-3),(-1,1)] then find matrix sum(r=0)^(oo) ((-1...

    Text Solution

    |

  9. Let p be a non singular matrix, and I + P + p^2 + ... + p^n = 0, then ...

    Text Solution

    |

  10. If A and B are square matrices of same order such that AB=O and B ne O...

    Text Solution

    |

  11. If A is a symmetric matrix, B is a skew-symmetric matrix, A+B is nonsi...

    Text Solution

    |

  12. If the matrices, A, B and (A+B) are non-singular, then prove that [A(A...

    Text Solution

    |

  13. If matrix a satisfies the equation A^(2)=A^(-1), then prove that A^(2^...

    Text Solution

    |

  14. If a and B are non-singular symmetric matrices such that AB=BA, then p...

    Text Solution

    |

  15. If A is a matrix of order n such that A^(T)A=I and X is any matric suc...

    Text Solution

    |

  16. Show that two matrices A=[(1,-1,0),(2,1,1)] and B=[(3,0,1),(0,3,1)] ...

    Text Solution

    |

  17. Using elementary transformations, find the inverse of the matrix : ...

    Text Solution

    |

  18. Let a be a 3xx3 matric such that [(1,2,3),(0,2,3),(0,1,1)]=[(0,0,1),...

    Text Solution

    |

  19. Using matrix method, solve the following system of equations: x+2y+z...

    Text Solution

    |

  20. Using matrix method, show that following system of equation is inconsi...

    Text Solution

    |