Home
Class 12
MATHS
Let a be a matrix of order 2xx2 such tha...

Let a be a matrix of order `2xx2` such that `A^(2)=O`.
`(I+A)^(100) =`

A

100 A

B

`100 (I+A)`

C

`100 I+A`

D

`I+100 A`

Text Solution

Verified by Experts

The correct Answer is:
D
`(I+A)^(100)= .^(100)C_(0)I^(100)+.^(100)C_(1)I^(99)A+.^(100)C_(2)I^(98) A^(2)+ +.^(100)C_(100)A^(100)`
`=I+100 A+O+O+ +O`
`=I+100 A`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise (Matrix)|5 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Numerical)|24 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Multiple)|33 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

Let a be a matrix of order 2xx2 such that A^(2)=O . tr (A) 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

Let A be a matrix of order 3xx3 such that |A|=3 . Let B=3A^(-1) and C =(adjA)/(2) , then the value of |A^(2)B^(3)C^(4)| is

If A is a square matrix of order 2 xx 2 such that A^(2)=O then,

Let A be a matrix of order 3 such that A^(2)=3A-2I where, I is an identify matrix of order 3. If A^(5)=alphaa+betaI , then alphabeta is equal to

Let A be a square matrix of order 2 such that A^(2)-4A+4I=0 , where I is an identity matrix of order 2. If B=A^(5)+4A^(4)+6A^(3)+4A^(2)+A-162I , then det(B) is equal to _________

If A is a matrix of order mxx m such that A^(2) +A + 2I = O , then

If A is a non singular matrix and I is a unit matrix of order same as A such that A^(2)+A-I=O , then A^(-1) is equal to

CENGAGE-MATRICES-Exercise (Comprehension)
  1. Let a be a matrix of order 2xx2 such that A^(2)=O. A^(2)-(a+d)A+(ad-...

    Text Solution

    |

  2. Let a be a matrix of order 2xx2 such that A^(2)=O. tr (A) is equal t...

    Text Solution

    |

  3. Let a be a matrix of order 2xx2 such that A^(2)=O. (I+A)^(100) =

    Text Solution

    |

  4. If A and B are two square matrices of order 3xx3 which satify AB=A and...

    Text Solution

    |

  5. if A and B are two matrices of order 3xx3 so that AB=A and BA=B then (...

    Text Solution

    |

  6. If A and B are two square matrices of order 3xx3 which satisfy AB=A an...

    Text Solution

    |

  7. Consider an arbitarary 3xx3 non-singular matrix A[a("ij")]. A maxtrix ...

    Text Solution

    |

  8. Let A=[a("ij")] be 3xx3 matrix and B=[b("ij")] be 3xx3 matrix such tha...

    Text Solution

    |

  9. Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-1)+A^(2)-I for n ...

    Text Solution

    |

  10. Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-1)+A^(2)-I for n ...

    Text Solution

    |

  11. Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-2)+A^(2)-I for n ...

    Text Solution

    |

  12. Let for A=[(1,0,0),(2,1,0),(3,2,1)], there be three row matrices R(1),...

    Text Solution

    |

  13. Let for A=[(1,0,0),(2,1,0),(3,2,1)], there be three row matrices R(1),...

    Text Solution

    |

  14. A and B are square matrices such that det. (A)=1, B B^(T)=I, det (B) g...

    Text Solution

    |

  15. A and B are square matrices such that det. (A)=1, B B^(T)=I, det (B) g...

    Text Solution

    |

  16. Let A be an mxxn matrix. If there exists a matrix L of type nxxm such ...

    Text Solution

    |

  17. Let A be an mxxn matrix. If there exists a matrix L of type nxxm such ...

    Text Solution

    |

  18. Let A be an mxxn matrix. If there exists a matrix L of type nxxm such ...

    Text Solution

    |