Home
Class 12
MATHS
If A^3=O ,t h e nI+A+A^2 equals a.I-A b....

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

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 z=(i)^((i)^(i)) w h e r e i=sqrt(-1),t h e n|z| is equal to a. 1 b. e^(-pi//2) c. e^(-pi) d. none of these

If A and B are two non-singular matrices such that A B=C ,t h e n,|B| is equal to a. (|C|)/(|A|) b. (|A|)/(|C|) c. |C| d. none of these

Let f(x)=(1+x)/(1-x) . If A is matrix for which A^3=0 ,then f(A) is (a) I+A+A^2 (b) I+2A+2A^2 (c) I-A-A^2 (d) none of these

If A is an orthogonal matrix then A^(-1) equals a. A^T b. A c. A^2 d. none of these

ifint(dx)/(x^2(x^n+1)^(((n-1)/n)) )=-[f(x)]^(1/n)+c ,t h e nf(x)i s (a) (1+x^n) (b) 1+x^(-1) (c) x^n+x^(-n) (d) none of these

If |z| < sqrt(2)-1,t h e n|z^2+2zcosalpha|i s a. less than 1 b. sqrt(2)+1 c. sqrt(2)-1 d. none of these

If Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. I-(2^n-1)Z d. none of these

ifint(dx)/(x^2(x^n+1)^(((n-1)/n))=-[f(x)]^(1/n)+c ,t h e nf(x)i s (1+x^n) (b) 1+x^(-1) x^n+x^(-n) (d) none of these

If A^(3)=O , then prove that (I-A)^(-1) =I+A+A^(2) .

In triangle A B C ,/_A=30^0,H is the orthocenter and D is the midpoint of B C . Segment H D is produced to T such that H D=D T The length A T is equal to (a). 2B C (b). 3B C (c). 4/2B C (d). none of these

CENGAGE PUBLICATION-MATRICES-All Questions
  1. If A is a square matrix of order n such that |a d j(a d jA)|=|A|^9, th...

    Text Solution

    |

  2. If A is order 3 square matrix such that |A|=2, then |(adj(adj(adjA)))|...

    Text Solution

    |

  3. 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...

    Text Solution

    |

  4. Evaluate int (1)/((x+1)sqrt(x-2))dx.

    Text Solution

    |

  5. (-A)^(-1) is always equal to (where A is nth-order square matrix) a. (...

    Text Solution

    |

  6. The matrix X for which [[1,-4],[ 3,-2]]X=[[-16-,6],[ 7 ,2]] is a.[[-2,...

    Text Solution

    |

  7. If A=[(0,-tan (alpha/2)),(tan (alpha/2),0)] and I is 2 xx 2 unit matri...

    Text Solution

    |

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

    Text Solution

    |

  9. If [[a, b],[ c,1-a]] is an idempotent matrix and f(x)=x-x^2 , bc=1/4 ...

    Text Solution

    |

  10. Let x be the solution set of equation A^x=I ,where A+[(0, 1,-1),(4,-3,...

    Text Solution

    |

  11. If A=[[alpha,0],[ 1, 1]] and B=[[1, 0],[ 5, 1]], find the values of al...

    Text Solution

    |

  12. Let a and b be two real numbers such that a > 1, b >1. If A=((a,0),(0,...

    Text Solution

    |

  13. Let f(x)=(1+x)/(1-x) . If A is matrix for which A^3=0,then f(A) is (a)...

    Text Solution

    |

  14. A and B are square matrices and A is non-singular matrix, then (A^(-1)...

    Text Solution

    |

  15. If A is a singular matrix, then adj A is

    Text Solution

    |

  16. The inverse of a diagonal matrix is a. a diagonal matrix              ...

    Text Solution

    |

  17. If P is non-singular matrix, then value of adj(P^(-1)) in terms of P i...

    Text Solution

    |

  18. If adjB=A ,|P|=|Q|=1, then. adj(Q^(-1)B P^(-1)) is a.P Q b. Q A P c...

    Text Solution

    |

  19. If A is non-singular and (A-2I)(A-4I)=0 , then ,1/6A+4/3A^(-1) is equa...

    Text Solution

    |

  20. If A(alpha,beta)=[[cosalpha,sinalpha,0],[-sinalpha,cosalpha,0],[ 0, 0,...

    Text Solution

    |