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

If `A^2-A +I = 0`, then the inverse of A is: (A) `A+I` (B) `A` (C) `A-I` (D) `I-A`

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

  • MATRICES

    CENGAGE|Exercise Exercise (Multiple)|33 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Comprehension)|18 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.5|17 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

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

Find the multiplicative inverse of -i .

Find the multiplicative inverse of 4-3i .

Find the multiplicative inverse of 2-3i.

Multiplicative inverse of 1 + i is ………..

Match column I (enzyme) with column II (characteristic/activity) and select the correct answer from the given codes, {:(Column I,Column II),(A."Taq DNA polymerase",(i)"Cleaves the ends of linear DNA"),(B."Exonuclease",(ii)"Breakdown of fungal cell wall"),(C."Protease",(iii)"Stable above" 90^(@)C),(D."Chitinase",(iv)"Made only by eukaryotic cells"),(,(v)"Degradation of proteins"):} 1) A − ( i i i ) , B − ( i v ) , C − ( i ) , D − ( i i ) 2) A − ( i v ) , B − ( i i i ) , C − ( i ) , D − ( i i ) 3) A − ( i i ) , B − ( i ) , C − ( v ) , D − ( i i i ) 4) A − ( i i i ) , B − ( i ) , C − ( v ) , D − ( i i )

Match column I with column II and select the correct answer from the given codes. {:(Column I, Column II),(A."Recombinant DNA",(i)"Chilled ethanol"),(B."Precipitation of DNA",(ii)DNA "staining"),(C."Transposons",(iii)"Jumping genes"),(D."Ethidium bromide",(iv)"Genetic engineering"):} 1) A − ( i v ) , B − ( i ) , C − ( i i i ) , D − ( i i ) 2) A − ( i ) , B − ( i i i ) , C − ( i i ) , D − ( i v ) 3) A − ( i i ) , B − ( i ) , C − ( i i i ) , D − ( i v ) 4) A − ( i v ) , B − ( i i ) , C − ( i ) , D − ( i i i )

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)

Let f(x)=(1+x)/(1-x) . If A is matrix for which A^3=O ,t h e nf(A) is (a) I+A+A^2 (b) I+2A+2A^2 (c) I-A-A^2 (d) none of these

The alleles I^(A) " and " I^(B) are _______

CENGAGE-MATRICES-Exercise (Single)
  1. If A=[a("ij")](4xx4), such that a("ij")={(2",","when "i=j),(0",","when...

    Text Solution

    |

  2. A is an involuntary matrix given by A=[(0, 1,-1), (4,-3, 4), (3,-3, 4)...

    Text Solution

    |

  3. If A is a nonsingular matrix such that A A^(T)=A^(T)A and B=A^(-1) A^(...

    Text Solution

    |

  4. If P is an orthogonal matrix and Q=P A P^T an dx=P^T A b. I c. A^(100...

    Text Solution

    |

  5. If Aa n dB are two non-singular matrices of the same order such that B...

    Text Solution

    |

  6. If adjB=A ,|P|=|Q|=1,t h e na d j(Q^(-1)B P^(-1)) is P Q b. Q A P c. P...

    Text Solution

    |

  7. If A is non-singular and (A-2I)(A-4I)=O ,t h e n1/6A+4/3A^(-1) is equa...

    Text Solution

    |

  8. Let f(x)=(1+x)/(1-x) . If A is matrix for which A^3=O ,t h e nf(A) is ...

    Text Solution

    |

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

    Text Solution

    |

  10. If A^2-A +I = 0, then the inverse of A is: (A) A+I (B) A (C) ...

    Text Solution

    |

  11. If F(x)=[("cos"x,-sin x,0),(sin x,cos x,0),(0,0,1)] and G(y)=[(cos y,0...

    Text Solution

    |

  12. If Aa n dB are square matrices of the same order and A is non-singular...

    Text Solution

    |

  13. 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

    |

  14. Given that matrix A[(x,3,2),(1,y,4),(2,2,z)]. If xyz=60 and 8x+4y+3z=2...

    Text Solution

    |

  15. Let A=[(1,2,3),(2,0,5),(0,2,1)] and B=[(0),(-3),(1)]. Which of the fol...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |