Home
Class 11
MATHS
Let A be 2xx2 matrix. Statement : adj(ad...

Let A be `2xx2` matrix. Statement : `adj(adjA)=A` Statement -2: `|adjA|=|A|`

A

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

B

Statement - 1 is true, Statement -2 is false

C

Statement -1 is false, Statement - 2 is true

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    AAKASH SERIES|Exercise INVERSE OF A MATRIX- PRACTICE EXERCISE|13 Videos

  • MATRICES

    AAKASH SERIES|Exercise LINEAR EQUATIONS - EXERCISE - I|24 Videos

  • MATRICES

    AAKASH SERIES|Exercise INVERSE OF A MATRIX- EXERCISE - I|21 Videos

  • MATHEMATICAL INDUCTION

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)|55 Videos

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos

Similar Questions

Explore conceptually related problems

Statement 1 : If A is nxxn matrix then |"adj (adj(adjA))|=|A|^((n-1)^(3)) Statement 2 |"adj A"|=|A|^(n)

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

Let A be 2xx2 matrix with non zero entries and let A^(2)=I where I is 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 4xx4 matrix and detA=-2 then det (AdjA)=

If A is a 3xx3 matrix and det(AdjA)=4 then detA=

If A is a 3xx3 matrix and det A=5 then det (AdjA)=

If A is a 4xx4 matrix and det (AdjA)=-27 then detA=

If a is a square matrix, then adjA^(T)-(adjA)^(T)=

Let A be 3xx3 matrix such A^(2)-5A+7I=0 statement 1 : A^(-1)=(1)/(7)(5I-A) Statement 2 : The polynomial A^(3)-2A^(2)-3A+I can be reduce to 5 (A-4I) then

If A is a nonsingular matrix of type n Adj(AdjA)=kA , then k=

AAKASH SERIES-MATRICES -INVERSE OF A MATRIX- EXERCISE - II
  1. If 3A=[(1,2,2),(2,1,-2),(-2,2,-1)] then A^(-1)=

    Text Solution

    |

  2. If A is non - singular and A^(2)-5A+7I=0 then I =

    Text Solution

    |

  3. If A is non Singular and (A-2I)(A-4I)=0 then 1/6A+4/3A^(-1)=

    Text Solution

    |

  4. A square nonsingular matrix satisfies A^(2)-A+2I=0 then A^(-1)=

    Text Solution

    |

  5. If A!=A^(2)=I then |I+A|=

    Text Solution

    |

  6. If A is a 3xx3 matrix and B is its Adjoint matrix. If the determinent ...

    Text Solution

    |

  7. If A is 4xx4 matrix and |2A|=64,B="Adj A" then |"Adj B"|=

    Text Solution

    |

  8. If A!=I is an idempotent matrix, then A is a

    Text Solution

    |

  9. If A is an orthogonal matrix then |A| is

    Text Solution

    |

  10. If A and B are two square matrices such that B=-A^(-1)BA then (A+B)^(2...

    Text Solution

    |

  11. The value of a third order determinant is 11 then the value of the squ...

    Text Solution

    |

  12. A and B are square matrices of order 3xx3, A is on orthogonal matrix a...

    Text Solution

    |

  13. Which of the following statements is false:

    Text Solution

    |

  14. Let A be 2xx2 matrix. Statement : adj(adjA)=A Statement -2: |adjA|=|A|

    Text Solution

    |

  15. If the product of the matrix B=[(2,6,4),(1,0,1),(-1,1,-1)] with a matr...

    Text Solution

    |

  16. If A is any square matrix of order 'n' Observe the following list {:...

    Text Solution

    |

  17. Statement 1 : If A is nxxn matrix then |"adj (adj(adjA))|=|A|^((n-1)^...

    Text Solution

    |

  18. The element of third row second column of the inverse of A=[(2,-4,-2),...

    Text Solution

    |

  19. If |{:(a(1),b(1),c(1)),(a(2),b(2),c(2)),(a(3),b(3),c(3)):}|=5, then th...

    Text Solution

    |

  20. If P=[(1, alpha, 3),(1,3,3),(2,4,4)] is the adjoint of a 3xx3 matrix A...

    Text Solution

    |