Home
Class 12
MATHS
If A^2-A+I=0, then the inverse of A is a...

If `A^2-A+I=0,` then the inverse of `A` is a. `A^(-2)` b. `A+I` c. `I-A` d. `A-I`

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`
or `I=A-A^(2)`
`IA^(-1)=A A^(-1)-A^(2)A^(-1)`
`implies A^(-1)=I-A`
Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

If A^(2)-A+I=0 then the inverse of the matrix A is

Find the multiplicative inverse of 2-3i.

Find the multiplicative inverse of 2-3i.

If A^2=I, then the value of det (A-I) is (where A has order 3) 1 b. -1 c. 0 d. cannot say anything

If x=1+i is a root of the equation x^3-i x+1-i=0, then the other real root is 0 b. 1 c. -1 d. none of these

If A is non-singular and (A-2I)(A-4I)=0 , then ,1/6A+4/3A^(-1) is equal to a. 0I b. 2I c. 6I d. I

If A^3=O ,t h e nI+A+A^2 equals a. I-A b. (I+A^1)^(-1) c. (I-A)^(-1) d. none of these

If A ,B ,A+I ,A+B are idempotent matrices, then A B is equal to a. B A b. -B A c. I d. O

If z^3+(3+2i)z+(-1+i a)=0 has one real root, then the value of a lies in the interval (a in R) a.(-2,1) b. (-1,0) c. (0,1) d. (-2,3)

If A is a nilpotent matrix of index 2, then for any positive integer n ,A(I+A)^n is equal to (a) A^(-1) (b) A (c) A^n (d) I_n

CENGAGE PUBLICATION-MATRICES-All Questions
  1. Let f(x)=(1+x)/(1-x) . If A is matrix for which A^3=0,then f(A) is (a)...

    Text Solution

    |

  2. Find the matrix A satisfying the matrix equation [{:(2,1),(3,2):}]A[...

    Text Solution

    |

  3. If A^2-A+I=0, then the inverse of A is a. A^(-2) b. A+I c. I-A d. A-I

    Text Solution

    |

  4. If f(x)=[(cosx,-sinx,0),(sinx ,cosx,0),(0,0,1)] and g(y)=[(cosy,0,siny...

    Text Solution

    |

  5. If k in Rot h e ndet{a d j(k In)} is equal to K^(n-1) b. K^(n(n-1)) c...

    Text Solution

    |

  6. Given the matrix A=[[x,3,2],[1,y,4],[2,2,z]]. If xyz=60 and 8x+4y+3z=2...

    Text Solution

    |

  7. Let A=[[1 ,2 ,3],[ 2, 0, 5],[ 0 ,2 ,1]] and B=[[0],[-3],[1]] . Which ...

    Text Solution

    |

  8. If A is a square matrix of order less than 4 such that |A-A^(T)| ne 0 ...

    Text Solution

    |

  9. Let A be a square matrix of order 3 such that det. (A)=1/3, then the v...

    Text Solution

    |

  10. If A and B are two non-singular matrices of order 3 such that A A^(T)=...

    Text Solution

    |

  11. If A is a square matric of order 5 and 2A^(-1)=A^(T), then the remaind...

    Text Solution

    |

  12. Let P=[(1,2,1),(0,1,-1),(3,1,1)]. If the product PQ has inverse R=[(-1...

    Text Solution

    |

  13. If A is unimodular, then which of the following is unimodular? a. -A ...

    Text Solution

    |

  14. Let A=a0 be a matrix of order 3, where a(i j)=x ; ifi=j ,x in R, 1 if...

    Text Solution

    |

  15. If A=[1-1 2 1],B=[a1b-1]a n d(A+B)^2=A^2+b^2+2A B ,t h e n a=-1 b. a=...

    Text Solution

    |

  16. If A B=Aa n dB A=B , then which of the following is/are true? A is ide...

    Text Solution

    |

  17. If A(theta)=[(sin theta, i cos theta),(i cos theta, sin theta)], then ...

    Text Solution

    |

  18. Let Aa n dB be two nonsingular square matrices, A^T a n dB^T are the t...

    Text Solution

    |

  19. If B is an idempotent matrix, and A=I-B , then A^2=A b. A^2=I c. A B=O...

    Text Solution

    |

  20. Suppose a(1), a(2), .... Are real numbers, with a(1) ne 0. If a(1), a(...

    Text Solution

    |