Home
Class 12
MATHS
Let A be a 2xx2 matrix Statement -1 ad...

Let A be a `2xx2` matrix
Statement -1 adj `(adjA)=A`
Statement-2 `abs(adjA) = abs(A)`

A

Statement -1 is true, Statement-2 is true, Statement-2 is a
correct explanation for Statement-1

B

Statement -1 is true, Statement - 2 is true, Statement -2 is not
a correct explanation for Statement-1

C

Statement-1 is true, Statement-2 is false

D

Statement-1 is false, Statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
B
`abs(adjA) = abs(A)^(n-1) = abs(A)^(2-1)=abs(A)`
`adj ("adj A")=abs(A)^(n-2)A`
`=abs(A)^(2-2) A= abs(A)^(0) A = A`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|14 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

Let A 2xx2 matrix A has determinant Find |adj(A)| if determinant of A Is 9

Statement -1 (Assertion) and Statement - 2 (Reason) Each of these examples also has four alternative choices, ONLY ONE of which is the correct answer. You have to select the correct choice as given below Statement-1 A is singular matrox pf order nxxn, then adj A is singular. Statement -2 abs(adj A) = abs(A)^(n-1)

If A is a square matrix of order 2, then adj (adj A)

Let a be a 2xx2 matrix with non-zero entries and let A^(2)=I , where I is a 2xx2 identity matrix. Define Tr(A)= sum of diagonal elements of A and |A| = determinant of matrix A. Statement 1 : Tr (A) = 0 Statement 2 : |A|=1

If A is a square matrix of order 3xx3 and abs(A) = 5 then abs (Adj. A) is :

If A is a matrix of order 3xx3 and abs (A) = 10 then abs (adj. A) is

Statement-1 (Assertion and Statement- 2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. Statement- 1 If A, B, C are matrices such that abs(A_(3xx3))=3, abs(B_(3xx3))= -1 and abs(C_(2xx2)) = 2, abs(2 ABC) = - 12. Statement - 2 For matrices A, B, C of the same order abs(ABC) = abs(A) abs(B) abs(C).

Statement-1 If a set A has n elements, then the number of binary relations on A = n^(n^(2)) . Statement-2 Number of possible relations from A to A = 2^(n^(2)) . (a) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1 (b) Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1 (c) Statement-1 is true, Statement-2 is false (d) Statement-1 is false, Statement-2 is true

Statement-1 (Assertion and Statement- 2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. Statement-1 For a singular matrix A , if AB = AC rArr B = C Statement-2 If abs(A) = 0, thhen A^(-1) does not exist. a. Statement- is true, Statement -2 is true, Statement-2 is a correct explanation for Statement-1 b. Statement-1 is true, Statement-2 is true, Sttatement - 2 is not a correct explanation for Stamtement-1 c. Statement 1 is true, Statement - 2 is false d. Statement-1 is false, Statement-2 is true

ARIHANT MATHS-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  2. The number of 3xx3 matrices A whose are ether 0 or 1 and for which t...

    Text Solution

    |

  3. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

    Text Solution

    |

  4. The number of 3xx3 matrices a whose entries are either 0 or 1 and for ...

    Text Solution

    |

  5. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

    Text Solution

    |

  6. Let p be an odd prime number and T(P) be the following set of 2xx2 m...

    Text Solution

    |

  7. Let p be an odd prime number and T(P) be the following set of 2xx2 m...

    Text Solution

    |

  8. Let K be a positive real number and A=[(2k-1,2sqrt(k),2sqrt(k)),(2sqrt...

    Text Solution

    |

  9. The number of 3 x 3 non-singular matrices, with four entries as 1 and ...

    Text Solution

    |

  10. Let a be a 2xx2 matrix with non-zero entries and let A^(2)=I, where I ...

    Text Solution

    |

  11. Let M and N be two 3xx3 nonsingular skew-symmetric matrices such that ...

    Text Solution

    |

  12. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

    Text Solution

    |

  13. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

    Text Solution

    |

  14. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

    Text Solution

    |

  15. Let omega!=1 be cube root of unity and S be the set of all non-singula...

    Text Solution

    |

  16. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

    Text Solution

    |

  17. Let A and B two symmetric matrices of order 3. Statement 1 : A(BA) a...

    Text Solution

    |

  18. Let P=[a(i j)] be a 3xx3 matrix and let Q=[b(i j)],w h e r eb(i j)=2^(...

    Text Solution

    |

  19. If P is a 3xx3 matrix such that P^T = 2P+I, where P^T is the transpose...

    Text Solution

    |

  20. If the adjoint of a 3x3 matrix P is (1 4 4) (2 1 7) (1 1 3) , t...

    Text Solution

    |