Home
Class 12
MATHS
If A ^2 −A+I=0 then A^(−1 ) =...

If ` A ^2 −A+I=0 ` then `A^(−1 )` =

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

A square non-singular matrix A satisfies A^2-A+2I=0," then "A^(-1) =

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

If A^2+A+I=0 , then A is non-singular A!=0 (b) A is singular A^(-1)=-(A+I)

If A=[(i,0), (0,i)],\ n in N , then A^(4n) equals [(0,i), (i,0)] (b) [(0 ,0) ,(0, 0)] (c) [(1, 0) ,(0, 1)] (d) [(0,i) ,(i,0)]

If A[{:(2,3),(1,2):}] satisfy the equation A^2-kA+I=0 , then find k also A^(-1) .

If A A=[3-2 4-2] and I=[1 0 0 1] , find k so that A^2=k A-2I .

If A=[[3,1],[-1,2]], I=[[1,0],[0,1]] and O=[[0,0],[0,0]] , show that A^2-5A+7I=0 . Hence find A^(-1) .

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 , 2) , (1, -1)] and I = [(1,0) , (0, 1)] , find the scalar k so that A^2 +I = kA .

If A = [ (-3 , 2) , (1, -1)] and I = [(1,0) , (0, 1)] , find the scalar k so that A^2 +I = kA .

ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Solve : cos ^(−1)(cos( (7π)/6) )

    Text Solution

    |

  2. The number of integral values of k for which the equation sin ^−1 x+t...

    Text Solution

    |

  3. If A ^2 −A+I=0 then A^(−1 ) =

    Text Solution

    |

  4. The number of solution of the equation 2[x] = x + 1 + {x} is/are a. 1 ...

    Text Solution

    |

  5. Solve : tan ^(−1) (tan((3π)/4))=

    Text Solution

    |

  6. Solve: tan ^ (-1)tan((2pi)/3))

    Text Solution

    |

  7. Draw the graph of the following function: f(x)=sin^(-1)(x+2)

    Text Solution

    |

  8. Draw the graph of the following function: g(x)=cos^(-1)x

    Text Solution

    |

  9. Draw the graph of the following function: h(x)=|tan^(-1)(3x)|\

    Text Solution

    |

  10. If f(x) = cos^(-1)x + cos^(-1){(x)/(2)+(1)/(2)sqrt(3-3x^(2))} then :

    Text Solution

    |

  11. If cos^(-1)x/a+cos^(-1)y/b=alpha , then (x^2)/(a^2)-(2x y)/(a b)cosalp...

    Text Solution

    |

  12. Prove that : sin^(-1)3/5+sin^(-1)8/(17)=sin^(-1)(77)/(85)

    Text Solution

    |

  13. cos^(- 1)x=2sin^(- 1)sqrt((1-x)/2)=2cos^(- 1)sqrt((1+x)/2)

    Text Solution

    |

  14. Prove: tan^(-1)2/3=1/2tan^(-1)(12)/5

    Text Solution

    |

  15. If sin^2x + sin^2y < 1 ; x, y in R then prove that sin^-1(tanx . tany...

    Text Solution

    |

  16. If a > b > c >0 , prove that cot^(-1)((a b+1)/(a-b))+cot^(-1)((b c+1)...

    Text Solution

    |

  17. Let cos^(-1) (x) + cos^(-1) (2x) + cos^(-1) (3x) " be " pi. If x satis...

    Text Solution

    |

  18. If alpha=2 arc t a n((1+x)/(1-x)) in B=a r c s i n((1-x^2)/(1+x^2))...

    Text Solution

    |

  19. Solve the following: sin^(-1)x+sin^(-1)2x=pi/3 (ii) cos^(-1)x+sin^(-1)...

    Text Solution

    |

  20. Arithmetic mean of the non-zero solutions of the equation tan^-1 (1/(2...

    Text Solution

    |