Home
Class 12
MATHS
Let A be a square matrix all of whose en...

Let A be a square matrix all of whose entries are integers.
Which one of the following it true?

A

If `det(A)=pm1`, then `A^(-1)` need not exist

B

If `det(A)=pm1`, then `A^(-1)` exist but all its entries are not necessarily integers

C

if `det(A)=pm1` , then `A^(-1)` exist but all its entries are non-integers

D

If `det(A)=pm1`, then `A^(-1)` exist but all its entries are integers

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|78 Videos

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|15 Videos

  • JEE MAIN REVISON TEST-23

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • MOCK TEST 1

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|10 Videos

Similar Questions

Explore conceptually related problems

Let A be a square matrix all of whose entries are integers. Then which one of the following is true? (1) If d e t A""=+-1,""t h e n""A^(1) exists but all its entries are not necessarily integers (2) If d e t A!=""+-1,""t h e n""A^(1) exists and all its entries are non-integers (3) If d e t A""=+-1,""t h e n""A^(1) exists and all its entries are integers (4) If d e t A""=+-1,""t h e n""A^(1) need not exist

Let A be a square matrix all of whose entries are integers. Then which one of the following is true? (1) If d e t A""=+-1,""t h e n""A^(1) exists but all its entries are not necessarily integers (2) If d e t A!=""+-1,""t h e n""A^(1) exists and all its entries are non-integers (3) If d e t A""=+-1,""t h e n""A^(1) exists and all its entries are integers (4) If d e t A""=+-1,""t h e n""A^(1) need not exist

Which one of the following is not true?

In n is an even integer, which one of the following is an odd integer?

Let A be an inbertible matrix. Which of the following is not true?

If x is integer and x^2 is even, which of the following must be true?

Let f(x)=[x]= Greatest integer less than or equal to x and k be an integer. Then, which one of the following in not correct?

If A is a nilpotent matrix of odd order r , then which of the following is true?

Let A be a square matrix of order 3 times 3 , then abs(kA) is equal to

If a, b, and c are consecutive integers and a < b < c, which one of the following must be true?

VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE MAIN ARCHIVE
  1. Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identity...

    Text Solution

    |

  2. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

    Text Solution

    |

  3. Let A be a square matrix all of whose entries are integers. Which on...

    Text Solution

    |

  4. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

    Text Solution

    |

  5. Let A= [[5,5alpha,alpha],[0,alpha,5alpha],[0,0,5]] . If |A^2|...

    Text Solution

    |

  6. If A and B f are square matrices of size nxxn such that A^(2) - B^(2...

    Text Solution

    |

  7. Let A =((1,2),(3,4))and B= ((a,0),(0,b)), a, bin N. Then,

    Text Solution

    |

  8. If A is a square matrix such that A^2-A+l=0, then the inverse of A is

    Text Solution

    |

  9. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

    Text Solution

    |

  10. The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 ...

    Text Solution

    |

  11. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

    Text Solution

    |

  12. Let A=[(0,0,-1),(0,-1,0),(-1,0,0)] Then only correct statement about t...

    Text Solution

    |

  13. Let A=[(1,-1,1),(2,1,-3),(1,1,1)] and 10 B=[(4,2,2),(-5,0,alpha),(1,-2...

    Text Solution

    |

  14. If the system of linear equations {:(x+2ay+az=0),(x+3by+bz=0),(x+4cy...

    Text Solution

    |

  15. If A=[{:(a,b),(b,a):}] and A^(2)=[{:(alpha, beta),(beta, alpha):}] the...

    Text Solution

    |

  16. If omega is a non-real cube root of unity and n is not a multiple o...

    Text Solution

    |

  17. if a,b,c are positive and are the pth qth and rth terms respectively ...

    Text Solution

    |

  18. If one of the cube roots of 1 be omega, then |(1,1+omega^2,omega^2),(...

    Text Solution

    |

  19. If A is a symmetric matrix and B is a skew-symmetric matrix such that ...

    Text Solution

    |

  20. The total number of matrices A = [{:(0, 2y, 1), (2x, y, -1), (2x, -y,...

    Text Solution

    |