Home
Class 12
MATHS
If A is a non -singular matrix such that...

If A is a non -singular matrix such that `A^(3)=A+l`, then the inverse of `B=A^(6)-A^(5)` is

A

`A`

B

`A^(-1)`

C

`-A`

D

`-A^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given `B=A^(6)-A^(5)` where `A^(3)=A+l`
`impliesB=(A^(3))^(2)-A^(3)A^(2)=(A+l)^(2)-(A+l)A^(2)`
`impliesA^(2)+l^(2)+2Al-A^(3)-A^(2)l`
`=l+2A-(A+l)`
`impliesB=A`
`:.` Inverse of `B=A^(-1)`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|18 Videos

  • MATRICES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|18 Videos

  • MATHEMATICAL LOGIC

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|22 Videos

  • MHTCET 2007

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MATHEMATICS|50 Videos

Similar Questions

Explore conceptually related problems

If A is a non-singular matrix, then

If A is a non-singular matrix, then A (adj.A)=

If is a non-singular matrix, then det (A^(1))=

If A is a non-singular square matrix such that A^(2)-7A+5I=0, then A^(-1)

If A is non-singular matrix of order, nxxn,

If A is 3xx3 non-singular matrix such that A^(-1)+(adj.A)=0," then det "(A)=

If A is a non-singular matrix such that (A-2I)(A-4I)=0 , then (A+ 8 A^(-1)) = .....

If A is a non-singular matrix of order 3, then |adjA^(3)|=

Let A be a non singular matrix of order 3times3 such that det A=5 and B is a non-singular matrix such that A^(-1)B^(2)+AB=0 .If the value of |A^(6)-2A^(4)B+A^(2)B^(2)|=N then log_(10)N=

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MATRICES-MISCELLANEOUS PROBLEMS
  1. If a matrix A is such that 3A^3 +2A^2+5A+I= 0, then A^(-1) is equal to

    Text Solution

    |

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

    Text Solution

    |

  3. If A is a non -singular matrix such that A^(3)=A+l, then the inverse o...

    Text Solution

    |

  4. If A is a skew symmetric matrix of order n and C is a column matrix of...

    Text Solution

    |

  5. If A and B are two square matrices such that AB=A and BA=B, then A^(2)...

    Text Solution

    |

  6. Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the fo...

    Text Solution

    |

  7. If A is a non-singular matrix of order 3, then adj(adj(A)) is equal to

    Text Solution

    |

  8. Let {:A=[(1,2),(-5,1)]and A^(-1)=xA+yI:}, then the values of x and y a...

    Text Solution

    |

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

    Text Solution

    |

  10. If A(theta)=[(1, than theta),(-tan, theta=1)] and AB=l, then (sec^(2)t...

    Text Solution

    |

  11. If A=[(cos alpha, -sin alpha, 0),(sin alpha, cos alpha,0),(0,0,1)] the...

    Text Solution

    |

  12. Suppose A is a matrix of order 3 and B=|A|A^(-1). If |A|=5, then |B| i...

    Text Solution

    |

  13. if[{:(2,1),(3,2):}]A[{:(-3,2),(5,-3):}]=[{:(1,0),(0,1):}],"then" A=?

    Text Solution

    |

  14. If f(theta)=[(cos theta, -sin theta,0),(sin theta, cos theta, 0),(0,0,...

    Text Solution

    |

  15. If A is a singular matrix, then Aadj(A) is a/an

    Text Solution

    |

  16. If k is a scalar and l is a unit matrix of order 3 then adj(kl) is equ...

    Text Solution

    |

  17. Consider the system of equations x+y+z=6 x+2y+3z=10 x+2y+lambda...

    Text Solution

    |

  18. Let a, b, c be any real numbers. Suppose that there are real numbers...

    Text Solution

    |

  19. Let a, b, c be positive real numbers. The following system of equation...

    Text Solution

    |

  20. If the system of linear equations x+2ay +az =0,x+3by+bz =0 and x+4cy ...

    Text Solution

    |