Home
Class 12
MATHS
If the matrix B is the adjoint of the sq...

If the matrix B is the adjoint of the square matrix A and `alpha` is the value of the determinant of A, then what is AB equal to ?

A

`alpha`

B

`((1)/(alpha))I`

C

I

D

`alpha I`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, adjoint of the square matrix A is B `rArr (B)/(|A|)=A^(-1)`
`rArr (AB)/(|A|)="AA"^(-1)=I`
`rArr AB = |A|I rArr AB = alpha I`
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

Adjoint OF square matrix

Let matrix B be the adjoint of a square matrix A, l be the identity matrix of the same order as A. If k ( ne 0) is the determinant of the matrix A, then what is AB equal to ?

Let matrix B be the adjoint of a square matrix A.I be the identity matrix of same order as A. If k(ne 0) is the determinant of the matrix A. then what is AB equal to ?

If D is the determinant of a square matrix A of order n, then the determinant of its adjoint is

If each element of a row of square matrix is doubled,then the determinant of the matrix is

If A is a square matrix of order 3 and |A|=-2 , then the value of the determinant |A||adjA| is

Write the adjoint of the matrix A=[(-3, 4),(7,-2)] .

Find the adjoint of the matrix: [(1,2),(3,4)]

Find the adjoint of the matrix A=[[2,3],[1,4]] .

If A is a 3x3 matrix and B is its adjoint matrix the determinant of B is 64 then determinant of A is

NDA PREVIOUS YEARS-MATRICES & DETERMINANTS-MQS
  1. The determinant |{:(a+b+c,a+b,a),(4a+3b+2c,3a+2b,2a),(10a+6b+3c,6a+3b,...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. 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

    |

  13. If adj A = [{:(a,0),(-1,b):}] and ab ne 0, then what is the value of |...

    Text Solution

    |

  14. If l + m + n = 0, then the system of equations -2x + y + z = l x -...

    Text Solution

    |

  15. If (a(1)//x)+(b(1)//y)=c(1),(a(2)//x)+(b(2)//y)=c(2) Delta(1)=|{:(a(1)...

    Text Solution

    |

  16. Show that |{:("sin"10^(@), -"cos"10^(@)), ("sin"80^(@), "cos"80^(@)):}...

    Text Solution

    |

  17. If |{:(2,4,0),(0,5,16),(0,0,1+p):}|=20, then what is the value of p?

    Text Solution

    |

  18. If the square matrices A and B are such that AB = A and BA = B, then

    Text Solution

    |

  19. If [{:(1,3),(0,1):}]A=[{:(1,-1),(0,1):}], then what is the matrix A ?

    Text Solution

    |

  20. Under which one of the following condition does the system of equation...

    Text Solution

    |