Home
Class 12
MATHS
Prove that ("adj. "A)^(-1)=("adj. "A^(-1...

Prove that `("adj. "A)^(-1)=("adj. "A^(-1))`.

Text Solution

Verified by Experts

`("adj. A")^(-1)=("adj. (adj. A)")/(|"adj. A"|)=(|A|^(n-1)A)/(|A|^(n-1))=A/(|A|)=("adj. "A^(-1))`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise (Single)|65 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Multiple)|33 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.4|12 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

Let A and B are two square matrices of order 3 such that det. (A)=3 and det. (B)=2 , then the value of det. (("adj. "(B^(-1) A^(-1)))^(-1)) is equal to _______ .

If A= [{:(8,-4),(-5," "3):}] , verify that A(adj A)= (adj A) A= |A|I_(2) .

If A=[[1,1,2],[1,2,2],[2,2,1]] verify that A(adj A) = (adj A)A = |A|I_(3) .

Prove that cos^(-1){(1+x)/2}=(cos^(-1)x)/2

Let A be a square matrix of order 3 such that det. (A)=1/3 , then the value of det. ("adj. "A^(-1)) is

Let A be a square matrix of order 3 such that adj. (adj. (adj. A)) =[(16,0,-24),(0,4,0),(0,12,4)] . Then find (i) |A| (ii) adj. A

If A and B are square matrices of order 3 such that det. (A) = -2 and det.(B)= 1 , then det.(A^(-1)adjB^(-1).adj(2A^(-1)) is equal to

If A and B are two non-singular matrices of order 3 such that A A^(T)=2I and A^(-1)=A^(T)-A . Adj. (2B^(-1)) , then det. (B) is equal to

Prove that ((sec A -1))/( (sec A+1) ) =((1-cos A)/((1+cos A ))

Prove that : (tanA)/(1-cotA)+(cotA)/(1-tanA)=1+secA" cosec"A

CENGAGE-MATRICES-Exercise 13.5
  1. By the method of matrix inversion, solve the system. [(1,1,1),(2,5,7...

    Text Solution

    |

  2. Let A=[[2,0,7] , [0,1,0], [1,-2,1]] and B=[[-x,14x,7x] , [0,1,0] , [x,...

    Text Solution

    |

  3. If A=[{:(0,1,1),(1,0,1),(1,1,0):}] show that A^(-1)=(1)/(2)(A^(2)=3I)

    Text Solution

    |

  4. For the matrix A=[3 1 7 5] , find x and y so that A^2+x I=y Adot

    Text Solution

    |

  5. If A^(3)=O, then prove that (I-A)^(-1) =I+A+A^(2).

    Text Solution

    |

  6. If A=[[cos alpha, -sin alpha] , [sin alpha, cos alpha]], B=[[cos2beta,...

    Text Solution

    |

  7. If A=[(1,2,2),(2,2,3),(1,-1,3)], C=[(2,1,1),(2,2,1),(1,1,1)], D=[(10),...

    Text Solution

    |

  8. If A is a 2xx2 matrix such that A^(2)-4A+3I=O, then prove that (A+3I)^...

    Text Solution

    |

  9. For two unimobular complex numbers z(1) and z(2), find [(bar(z)(1),-z(...

    Text Solution

    |

  10. Prove that inverse of a skew-symmetric matrix (if it exists) is skew-s...

    Text Solution

    |

  11. If square matrix a is orthogonal, then prove that its inverse is also ...

    Text Solution

    |

  12. If A is a skew symmetric matrix, then B=(I-A)(I+A)^(-1) is (where I is...

    Text Solution

    |

  13. Prove that ("adj. "A)^(-1)=("adj. "A^(-1)).

    Text Solution

    |

  14. Using elementary transformation, find the inverse of the matrix A=[(a,...

    Text Solution

    |

  15. Show that the two matrices A, P^(-1) AP have the same characteristic r...

    Text Solution

    |

  16. Show that the characteristics roots of an idempotent matris are either...

    Text Solution

    |

  17. If alpha is a characteristic root of a nonsin-gular matrix, then prove...

    Text Solution

    |