Home
Class 12
MATHS
If A is an invertible matrix of order 2,...

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ALGEBRA OF MATRICES

    RD SHARMA ENGLISH|Exercise All Questions|410 Videos

Similar Questions

Explore conceptually related problems

If A is an invertble 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 matrix then det(A^-1) is equal to (A) 1 (B) 1/|A| (C) |A| (D) none of these

If A is an invertible matrix then det(A^-1) is equal to (A) 1 (B) 1/|A| (C) |A| (D) none of these

If A is a matrix of order 3, then det(kA) is

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 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 matrix, then (a d jdotA)^(-1) is equal to a. a d jdot(A^(-1)) b. A/(d e tdotA) c. A d. (detA)A

For an invertible square matrix of order 3 with real entries A^-1=A^2 then det A= (A) 1/3 (B) 3 (C) 0 (D) 1

if A is a square matrix such that A^(2)=A, then det (A) is equal to

If A is a skew-symmetric matrix of order 3, then prove that det A = 0 .

RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists ...

    Text Solution

    |

  2. If for the matrix A ,\ A^3=I , then A^(-1)=(a)A^2 (b) A^3 (c) A (d) no...

    Text Solution

    |

  3. If Aa n dB are two square matrices such that B=-A^(-1)B A ,t h e n(A+B...

    Text Solution

    |

  4. If A=[(2 ,0 ,0),( 0 ,2 ,0),( 0 ,0 ,2)] , then A^5= (a) 5A (b) 10 A (c...

    Text Solution

    |

  5. For non-singular square matrix A ,\ B\ a n d\ C of the same order th...

    Text Solution

    |

  6. The matrix [(5 ,1 ,0), (3 ,-2 ,-4 ), (6 ,-1 ,-2b)] is a singular matri...

    Text Solution

    |

  7. If d is the determinant of a square matrix A of order n , then the ...

    Text Solution

    |

  8. If A is a matrix of order 3 and |A|=8 , then |a d j\ A|= (a) 1 (b)...

    Text Solution

    |

  9. If A^2-A +I = 0, then the inverse of A is: (A) A+I (B) A (C) ...

    Text Solution

    |

  10. If A and B are invertible matrices, which of the following statemen...

    Text Solution

    |

  11. If A is a square matrix such that A^2 = I, then A^(-1) is equal to (i...

    Text Solution

    |

  12. Let A=[(1, 2), (3,-5)] and B=[(1, 0), (0, 2)] and X be a matrix such t...

    Text Solution

    |

  13. If A=[ (2 , 3) ,( 5 ,-2 )] , then find |A|

    Text Solution

    |

  14. If A=1/3[(1,2,2),(2,1,-2),(x,2,y)] satisfies A^T A=I , then x+y= (a) ...

    Text Solution

    |

  15. If A=[(1,0,1), (0,0,1),(a,b,2)] , then a I+b A+2A^2 equals (a) A (b) -...

    Text Solution

    |

  16. If [(1,-tantheta),(tantheta,1)][(1,tantheta),(-tantheta,1)]^(-1)=[(a,-...

    Text Solution

    |

  17. If a matrix A is such that 3A^3 +2A^2+5A+I= 0, then A^(-1) is equal to

    Text Solution

    |

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

    Text Solution

    |

  19. If A=[(2,-1),( 3,-2)] , then A^n= [(1, 0),( 0,1)] , if (a) n is an ev...

    Text Solution

    |

  20. If x ,\ y ,\ z are non-zero real numbers, then the inverse of the ma...

    Text Solution

    |