Home
Class 12
MATHS
If A be an n-square matrix and B be its ...

If A be an n-square matrix and B be its adjoint, then show that `Det (AB + KI_(n)) = [Det (A) + K]^(n)`, where K is a scalar quantity.

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MOTION|Exercise Exercise - 1|35 Videos

  • MATRICES

    MOTION|Exercise Exercise - 2(Level-I) (Single 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

Let A be an nth-order square matrix and B be its adjoint,then |AB+KI_(n)| is (where K is a scalar quantity (|A|+K)^(n-2) b.(|A|+)K^(n) c.(|A|+K)^(n-1) d.none of these

If A is a nonsingular matrix satisfying AB-BA=A , then prove that det. (B+I)= det, (B-I) .

Let B is an invertible square matrix and B is the adjoint of matrix A such that AB=B^(T) . Then

If x is a non singular matrix and y is a square matrix,such that det(x^(-1)yx)=K det y ,then find K

Let A be a square matreix of order n then det(A)=det(A^(T))

If A is non-singular matrix satifying AB-BA=A, then prove that det(B+I)=det(B-I)

If A is a square matrix of order 2, then det(-3A) is A) 3 det A B) -3 det A C) 9 det A D) -9 det A

If A is 3x3 matrix and det adj(A)=k then det(adj2A)=

If A is matrix of order 3 xx 2 and B is matrix of order 2 xx 3 , then what is |kAB|equal to (where k is any scalar quantity)?

MOTION-MATRICES -Exercise - 4 (Level-II)
  1. If A be an n-square matrix and B be its adjoint, then show that Det (A...

    Text Solution

    |

  2. Let A=[1 0 0 0 1 1 0-2 4],I=[1 0 0 0 1 0 0 0 1]a n dA^(-1)=[1/6(A^2+c ...

    Text Solution

    |

  3. If P=[[sqrt3/2,1/2] , [-1/2,sqrt3/2]] and A=[[1,1] , [0,1]] and Q=PAP^...

    Text Solution

    |

  4. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

    Text Solution

    |

  5. Let A = [(1,0,0), (2,1,0), (3,2,1)], and U1, U2 and U3 are columns of ...

    Text Solution

    |

  6. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

    Text Solution

    |

  7. Match the following {:("(A) The minimum value of "(x^(2)+2x+4)/(x+2)...

    Text Solution

    |

  8. Let A be the set of all 3 xx 3 symmetric matrices all of whose entrie...

    Text Solution

    |

  9. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  10. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  11. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

    Text Solution

    |

  12. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

    Text Solution

    |

  13. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

    Text Solution

    |

  14. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

    Text Solution

    |

  15. Let K be a positive real number and A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1-...

    Text Solution

    |

  16. Let M be a 3xx3 matrix satisfying M[{:(0),(1),(0):}]=[{:(-1),(2),(3):}...

    Text Solution

    |

  17. Let P = [a(ij)] " be a " 3 xx 3 matrix and let Q = [b(ij)], " where " ...

    Text Solution

    |

  18. If P is a 3xx3 matrix such that P^T = 2P+I, where P^T is the transpose...

    Text Solution

    |

  19. If the adjoint of a 3 3 matrix P is 1 4 4 2 1 7 1 1 3 , then the po...

    Text Solution

    |

  20. For 3xx3 matrices Ma n dN , which of the following statement (s) is (a...

    Text Solution

    |

  21. Let Ma n dN be two 3xx3 matrices such that M N=N Mdot Further, if M!=N...

    Text Solution

    |