Home
Class 12
MATHS
If A^(2)-A+I=O, then A^(-1) is equal to...

If `A^(2)-A+I=O`, then `A^(-1)` is equal to

A

`a^(-2)`

B

`A + I`

C

`I - A`

D

`A - I`

Text Solution

Verified by Experts

The correct Answer is:
C
`A^(2) -A+I=0`
` rArr I=A-A^(2) rArr I = A(I-A)`
`rArr A^(-1) I = A^(-1) (A(I-A))rArr A^(-1) =I - A`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

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

  • MATHEMATICAL INDUCTION

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

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|29 Videos

Similar Questions

Explore conceptually related problems

If a matrix A is such that 3A^3 +2A^2+5A+I= 0 , then A^(-1) is equal to

If A is a square matrix such that A^2 = I , then A^(-1) is equal to (i) I (ii) 0 (iii) A (iv) I+A

If A=[(1,-3), (2,k)] and A^(2) - 4A + 10I = A , then k is equal to

if A=[a_(ij)]_(2*2) where a_(ij)={i+j , i!=j and i^2-2j ,i=j} then A^-1 is equal to

If A is non-singular and (A-2I)(A-4I)=O ,t h e n1/6A+4/3A^(-1) is equal to O I b. 2I c. 6I d. I

Let A be a square matrix such that A^2-A+I=O , then write A^(-1) in terms of Adot

If A=[(2, 2),(9,4)] and A^(2)+aA+bI=O . Then a+2b is equal to (where, I is an identity matrix and O is a null matrix of order 2 respectively)

Consider the matrix A=[(3,1),(-6,-2)] , then (I+A)^(40) is equal to

Let a be a matrix of order 2xx2 such that A^(2)=O . A^(2)-(a+d)A+(ad-bc)I is equal to

If A and B are two matrices of order 3 such that AB=O and A^(2)+B=I , then tr. (A^(2)+B^(2)) is equal to ________.

ARIHANT MATHS ENGLISH-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. about to only mathematics

    Text Solution

    |

  2. If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] then which one of the following...

    Text Solution

    |

  3. If A^(2)-A+I=O, then A^(-1) is equal to

    Text Solution

    |

  4. Let {:A=[(1,0,0),(2,1,0),(3,2,1)]:}and U1,U2,U3 be column matrices sat...

    Text Solution

    |

  5. Let A = [(1,0,0), (2,1,0), (3,2,1)], and U1, U2 and U3 are columns of ...

    Text Solution

    |

  6. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

    Text Solution

    |

  7. Let A=[{:(1,2),(3,4):}]and B = [{:(a,0),(0,b):}] where a, b are natura...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. Let A and B be 3xx3 matrtices of real numbers, where A is symmetric, "...

    Text Solution

    |

  11. Let A be a square matrix all of whose entries are integers. Then wh...

    Text Solution

    |

  12. Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identi...

    Text Solution

    |

  13. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  14. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  15. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |