Home
Class 11
MATHS
If A is an invertible matrix then det(A^...

If A is an invertible matrix then `det(A^-1)` is equal to

A

det (A)

B

`1/(det (A))`

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Section I - Assertion Reason Type|12 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|21 Videos

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA|Exercise Exercise|28 Videos

Similar Questions

Explore conceptually related problems

If A is an invertible matrix,tehn (adj.A)^(-1) is equal to adj.(A^(-1)) b.(A)/(det.A) c.A d.(det A)A

If A is invertible matrix. Then what is det (A^(-1)) equal to ?

If A is an invertible square matrix then |A^(-1)| =?

If A is an invertible matrix of order 2 then det (A^(-1)) is equal to (a) det (A) (b) (1)/(det(A))(c)1 (d) 0

If A is an invertible square matrix,then A^(T) is also invertible and (A^(T))^(-1)=(A^(-1))^(T)

If A is an invertible matrix of order 2, then det (A^(-1)) is equal to

If B is a non-singular matrix and A is a square matrix,then det (B^(-1)AB) is equal to (A)det(A^(-1))(B)det(B^(-1))(C)det(A)(D)det(B)

If A is an invertible symmetric matrix the A^-1 is A. a diagonal matrix B. symmetric C. skew symmetric D. none of these

If A is a invertible matrix of order 4 then |A^(-1)|=

OBJECTIVE RD SHARMA-MATRICES-Exercise
  1. If A is an orthogonal matrix, then

    Text Solution

    |

  2. Let A be a non-singular square matrix of order n. Then; |adjA| = |A|^(...

    Text Solution

    |

  3. Let A=[a(ij)](nxxn) be a square matrix of order 3 such that |A|=-7 an...

    Text Solution

    |

  4. If A is a non-singlular square matrix of order n, then the rank of A i...

    Text Solution

    |

  5. If A is a matrix such that there exists a square submatrix of order r ...

    Text Solution

    |

  6. Let A be a matrix of rank r. Then,

    Text Solution

    |

  7. Let A=[a(ij)](mxxn) be a matrix such that a(ij)=1 for all I,j. Then ,

    Text Solution

    |

  8. If A is a non-zero column matrix of order mxx1 and B is a non-zero row...

    Text Solution

    |

  9. The rank of the matrix {:[(1,2,3,0),(2,4,3,2),(3,2,1,3),(6,8,7,5)]:}, ...

    Text Solution

    |

  10. If A is an invertible matrix then det(A^-1) is equal to

    Text Solution

    |

  11. If A and B are two matrices such that rank of A = m and rank of B = n...

    Text Solution

    |

  12. If {:A=[(3,4),(2,4)],B=[(-2,-2),(0,-1)]:}," then " (A+B)^(-1)=

    Text Solution

    |

  13. Let {:A=[(a,0,0),(0,a,0),(0,0,a)]:}, then A^n is equal to

    Text Solution

    |

  14. If {:A=[(costheta,sintheta),(-sintheta,costheta)]:}, " then "lim(ntooo...

    Text Solution

    |

  15. If {:A=[(1,2,x),(0,1,0),(0,0,1)]andB=[(1,-2,y),(0,1,0),(0,0,1)]:} and ...

    Text Solution

    |

  16. If A=[{:(,1,a),(,0,1):}] then find underset(n-oo)(lim)(1)/(n)A^(n)

    Text Solution

    |

  17. If the matrix {:[(a,b),(c,d)]:} is commutative with matrix {:[(1,1),(...

    Text Solution

    |

  18. If {:A=[(1,0),(k,1)]andB=[(0,0),(k,0)]:} such that A^100-I=lambdaB," ...

    Text Solution

    |

  19. If matrix A has 180 elements, then the number of possible orders of A ...

    Text Solution

    |

  20. A 3xx3 matrix A, with 1st row elements as 2,-1,-1 respectively, is mod...

    Text Solution

    |