Home
Class 12
MATHS
If a, b, c are non-zero real numbers, t...

If `a, b, c` are non-zero real numbers, then the inverse of the matrix `A [[a,0,0],[0,b,0],[0,0,c]]` is

A

`[[a^-1,0,0],[0,b^-1,0],[0,0,c^-1]]`

B

`abc [[a^-1,0,0],[0,b^-1,0],[0,0,c^-1]]`

C

`(1)/(abc)[[1,0,0],[0,1,0],[0,0,1]]`

D

`(1)/(abc)[[a,0,0],[0,b,0],[0,0,c]]`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    HIMALAYA PUBLICATION|Exercise Question Bank|97 Videos

  • MAXIMA AND MINIMA

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|167 Videos

Similar Questions

Explore conceptually related problems

The inverse of the matrix A = [[2,0,0],[0,3,0],[0,0,4]] is

The inverse of the matrix A= [[0,1,0],[1,0,0],[0,0,1]] is A

The inverse of the matrix A=[(2,0,0),(0,3,0),(0,0,4)] is

The inverse of the matrix [[1 , 0, 0],[ a , 1 , 0],[ b, c , 1]] is

If x,y,z are nonzero real number , then the inverse of matrix A= {:[( x,0,0),( 0,y,0) ,( 0,0,z) ]:} is

The inverse of [[1,0,0],[0,2,0],[0,0,3]] is

The inverse of the matrix [(2,5,0),(0,1,1),(-1,0,3)] is

If a,b,c are positive real numbers, then the roots of the equation ax^(2) + bx + c =0

HIMALAYA PUBLICATION-MATRICES AND DETERMINANTS-QUESTION BANK
  1. If A=[[2,-1],[-1,2]]and I is the unit matrix of order 2, then A^2=

    Text Solution

    |

  2. The multiplicative inverse of the matrix A = [[0,0,1],[0,1,0],[1,0,0...

    Text Solution

    |

  3. If a, b, c are non-zero real numbers, then the inverse of the matrix ...

    Text Solution

    |

  4. If P= [[i,0,-i],[0,-i,i],[-i,i,0]], Q= [[-i,i],[0,0],[i, -i]] then P Q...

    Text Solution

    |

  5. If [[alpha,beta],[gamma,-alpha]] is to be square root of the two rowe...

    Text Solution

    |

  6. If A and B are square matrices of same order such that, (A+B)^2=A^2+B...

    Text Solution

    |

  7. The element in the first row and third column of the inverse of the ma...

    Text Solution

    |

  8. A^2-A+I=0, then the inverse of A is

    Text Solution

    |

  9. A is a 3 xx 3 matrix and B is its adjoint matrix. If |B|=81, then |A|=

    Text Solution

    |

  10. If A=[[a,0,0],[0,a,0],[0,0,a]] then |adj A|=

    Text Solution

    |

  11. For a 3xx 3 matrix A, if det A=3, then det (adj A)=

    Text Solution

    |

  12. If (1 x 2)[[1,2,3],[0,1,5],[0,2,3]] [[x],[-1],[2]]=0 then x=

    Text Solution

    |

  13. If A and B are two matrices such that A B=B and B A=A, then A^2+B^2=

    Text Solution

    |

  14. If A=[[3,-4],[1,-1]] then the value of A^n=

    Text Solution

    |

  15. If A is a square matrix of order n, then det (adj A)=

    Text Solution

    |

  16. For any 2xx 2 matrix A, if A . adj A = [[7,0],[0,7]] then |A| is equal...

    Text Solution

    |

  17. If A=[[1,-1,2],[2,1,-1],[-1,2,1]], then det [adj .(adj A)]=

    Text Solution

    |

  18. If A = [[1,0,0],[0,1,0],[0,0,1]], then A^2+2 A=

    Text Solution

    |

  19. If A = [[0,c,-b],[-c,0,a],[b,-a,0]] and B = [[a^(2),ab,ac],[ab,b^2,bc]...

    Text Solution

    |

  20. If the matrix A B is a zero matrix, then

    Text Solution

    |