Home
Class 12
MATHS
If A is a square matrix of order 3 such ...

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

A

`5^(3)xx4^(2)`

B

`5^(2)xx4^(3)`

C

`5^(2)xx16^(3)`

D

`5^(3)xx16^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `Adj(4A)=4^(2)Adj(A)=16Adj(A)`
`implies|Adj4A|=16^(3)=|AdjA|=16^(3)*5^(2)`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Multiple Correct Answer|7 Videos

  • MATRICES

    CENGAGE|Exercise JEE Advanced Previous Year|26 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 is a square matrix of order 3 such that |A|=2,t h e n|(a d jA^(-1))^(-1)| is ___________.

If A is a square matrix of order n, then |adj A|=

If A is a square matrix of order 3 then |kA| = ………………… .

If A is order 3 square matrix such that |A|=2 , then |"adj (adj (adj A))"| is

If A is order 2 square matrix such that |A|=2, then |(adj(adj(adjA)))| is 512 b. 256 c. 64 d. none of these

If A is a square matrix of order less than 4 such that |A-A^(T)| ne 0 and B= adj. (A), then adj. (B^(2)A^(-1) B^(-1) A) is

Which of the following is/are correct? (i) Adjoint of a symmetric matrix is is also a symmetric matrix (ii) Adjoint of a diagonal matrix is also a diagonal matrix. (iii) If A is a square matrix of order n and lamda is a scalar, then adj(lamdaA)=lamda^(n)adj(A) . (iv) A(adjA)=(adjA)A=|A|I

A be a square matrix of order 2 with |A| ne 0 such that |A+|A|adj(A)|=0 , where adj(A) is a adjoint of matrix A , then the value of |A-|A|adj(A)| is

Let A be a square matrix of order 3 such that det. (A)=1/3 , then the value of det. ("adj. "A^(-1)) is

CENGAGE-MATRICES-Single correct Answer
  1. The number of 2xx2 matrices A, that are there with the elements as rea...

    Text Solution

    |

  2. If the orthogonal square matrices A and B of same size satisfy detA+de...

    Text Solution

    |

  3. If A=[{:(costheta,sintheta),(sintheta,-costheta):}], B=[{:(1,0),(-1,1)...

    Text Solution

    |

  4. Let A be a 3xx3 matrix given by A=(a(ij))(3xx3). If for every column v...

    Text Solution

    |

  5. Suppose A and B are two non singular matrices such that B != I, A^6 = ...

    Text Solution

    |

  6. Let A be a 2xx3 matrix, whereas B be a 3xx2 amtrix. If det.(AB)=4, the...

    Text Solution

    |

  7. Let A be a square matrix of order 3 so that sum of elements of each ro...

    Text Solution

    |

  8. A and B be 3xx3 matrices such that AB+A=0, then

    Text Solution

    |

  9. If (A+B)^(2)=A^(2)+B^(2) and |A| ne 0 , then |B|= (where A and B are m...

    Text Solution

    |

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

    Text Solution

    |

  11. If A and B are symmetric and commute, then which of the following is/a...

    Text Solution

    |

  12. If A is a square matrix of order 3 such that |A|=2,t h e n|(a d jA^(-1...

    Text Solution

    |

  13. Let matrix A=[{:(x,y,-z),(1,2,3),(1,1,2):}] , where x,y,z in N. If |ad...

    Text Solution

    |

  14. A be a square matrix of order 2 with |A| ne 0 such that |A+|A|adj(A)|=...

    Text Solution

    |

  15. If S is a real skew-symmetric matrix and det. (I-S) ne 0, then prove t...

    Text Solution

    |

  16. If A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}] , then the trace of the matrix A...

    Text Solution

    |

  17. If A=[{:(1,-1,1),(0,2,-3),(2,1,0):}] and B=(adjA) and C=5A, then find ...

    Text Solution

    |

  18. Let A and B be two non-singular square matrices such that B ne I and A...

    Text Solution

    |

  19. If A is an idempotent matrix satisfying (I-0.4A)^(-1)=I-alphaA where I...

    Text Solution

    |

  20. If A and B are two non-singular matrices which commute, then (A(A+B)^...

    Text Solution

    |