Home
Class 12
MATHS
Let A=[a(ij)](nxxn) be a square matrix a...

Let `A=[a_(ij)]_(nxxn)` be a square matrix and let `c_(ij)` be cofactor of `a_(ij)` in A. If `C=[c_(ij)]`, then

A

`|A|^(m-1)`

B

`|A|^(m)`

C

`|A|^(m+1)`

D

Zero

Text Solution

Verified by Experts

The correct Answer is:
C

Let `A = [a_(ij)]_(m xx m)` be a matrix and `C = [c_(ij)]_(m xx m)` be another matrix where cij is the cofactor of `a_(ij)`.
`therefore` The value of `|AC|=|A|^(m+1)`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    NDA PREVIOUS YEARS|Exercise MCQ|59 Videos
  • PAIR OF STRAIGHT LINES

    NDA PREVIOUS YEARS|Exercise Example|12 Videos

Similar Questions

Explore conceptually related problems

Let A=[a_(ij)]_(n xx n) be a square matrix and let c_(ij) be cofactor of a_(ij) in A. If C=[c_(ij)], then

A = [a_(ij)]_(mxx n) is a square matrix , if

A matrix A=[a_(ij)]_(mxxn) is

Let A=[a_(ij)]_(3xx3) be a matrix such that a_(ij)=(i+2j)/(2) where i,j in [1, 3] and i,j inN . If C_(ij) be a cofactor of a_(ij), then the value of a_(11)C_(21)+a_(12)C_(22)+a_(13)C_(23)+a_(21)C_(31)+a_(22)C_(32)+a_(33)C_(33)+a_(31)C_(11)+a_(32)C_(12)+a_(33)C_(13) is equal to

If A=[a_(ij)]_(3xx3) is a scalar matrix such that a_(ij)=5" for all "i=j," then: "|A|=

In square matrix A=(a_(ij)) if i lt j and a_(ij)=0 then A is

If A=(a_(ij)) is a 4xx4 matrix and C_(ij) is the co-factor of the element a_(ij) in Det(A), then the expression a_(11)C_(11)+a_(12)C_(12)+a_(13)C_(13)+a_(14)C_(14) equals-

NDA PREVIOUS YEARS-MATRICES & DETERMINANTS-MQS
  1. For what value of p, is the system of equation p^3x+(p+1)^3y=(p+2)^3 a...

    Text Solution

    |

  2. If A=[{:(2x,0),(x,x):}]and A^(-1)=[{:(1,0),(-1,2):}], then what is the...

    Text Solution

    |

  3. Let A=[a(ij)](nxxn) be a square matrix and let c(ij) be cofactor of a...

    Text Solution

    |

  4. If omega is the cube root of unity, then what is one root of the equat...

    Text Solution

    |

  5. If A = [{:(2,2),(2,2):}], then what is A^(n) equal to ?

    Text Solution

    |

  6. If the least number of zeroes in a lower triangular matrix is 10, then...

    Text Solution

    |

  7. If the inverse of [{:(1,p,q),(0,x,0),(0,0,1):}]"is"[{:(1,-p,-q),(0,1,0...

    Text Solution

    |

  8. If AB=[{:(4,11),(4,5):}]and A=[{:(3,2),(1,2):}], then what is the valu...

    Text Solution

    |

  9. The determinant |{:(a+b+c,a+b,a),(4a+3b+2c,3a+2b,2a),(10a+6b+3c,6a+3b,...

    Text Solution

    |

  10. If X = [{:(1,-2),(0,3):}], and I is a 2 xx 2 identity matrix, then X^(...

    Text Solution

    |

  11. If the matrix B is the adjoint of the square matrix A and alpha is the...

    Text Solution

    |

  12. What is the determinant |{:(bc,a,a^(2)),(ca,b,b^(2)),(ab,c,c^(2)):}| e...

    Text Solution

    |

  13. If x^(2)+y^(2)+z^(2)=1, then what is the value of |{:(1,z,-y),(-z,1,x)...

    Text Solution

    |

  14. If |A(n xx n)|=3 and |"adj A"|=243, what is the value of n?

    Text Solution

    |

  15. Under what condition does A (BC) = (AB)C hold, where A, B, C are three...

    Text Solution

    |

  16. If A is matrix of order 3 xx 2 and B is matrix of order 2 xx 3, then w...

    Text Solution

    |

  17. If [{:(5,0),(0,7):}]^(-1)[{:(x),(-y):}]=[{:(-1),(2):}], then which on...

    Text Solution

    |

  18. Which one of the following statement is correct ? The system of linear...

    Text Solution

    |

  19. Suppose the system of equations a(1)x+b(1)y+c(1)z=d(1) a(2)x+b(2)y...

    Text Solution

    |

  20. If a,b,c are in G.P. then the value of |(a,b,a+b),(b,c,b+c),(a+b,b+c,0...

    Text Solution

    |