Home
Class 12
MATHS
Prove that: adj.In=In...

Prove that:
`adj.I_n=I_n`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE|588 Videos

  • EXCLUSIVELY FOR JEE(ADVANCED)

    MODERN PUBLICATION|Exercise EXERCISE|38 Videos

Similar Questions

Explore conceptually related problems

Prove that: adj.I_n^-1=I_n

Prove that: adj.O=O

If I_n is the area of n-s i d e d regular polygon inscribed in a circle of unit radius and O_n be the area of the polygon circumscribing the given circle, prove that I_n=(O_n)/2(sqrt(1+((2I_n)/n)^2))

Prove that : "^nP_n= 2^nP_(n-2) .

If I_n=int x^nsqrt(a^2-x^2)dx, prove that I_n=-(x^(n-1)(a^2-x^2)^(3/2))/((n+2))+((n+1))/((n+2))a^2I_(n-2)

Prove that I_(1),I_(2),I_(3)"..." form an AP, if I_(n)=int_(0)^(pi)(sin2nx)/(sinx)dx .

Prove that n! (n+2)=n!+(n+1)! .

Let A=[[0,1],[0,0]] , prove that: (aI+bA)^n = a^(n-1) bA , where I is the unit matrix of order 2 and n is a positive integer.

Prove that t a n(i(log)_e((a-i b)/(a+i b)))=(2a b)/(a^2-b^2)(w h e r ea ,b in R^+)

Prove that identity : sum_(i=1)^(n) (x_i-bar x)^2 = sum_(i=1)^(n) x_i^2-n bar x^2= sum_(i=1)^(n) x_i^2 -(sum_(i=1)^(n) x_i)^2/n .

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that: adj.In=In

    Text Solution

    |

  2. Let A be a square matrix of order 3xx3, then prove that |kA|=k|A|.

    Text Solution

    |

  3. If any two rows (or columns) of a determinant are identical, the value...

    Text Solution

    |

  4. Answer in one word. {:|(3,1,6),(5,2,10),(7,4,14)|

    Text Solution

    |

  5. If A is a square matrix of order 3 and |3A| = k|A|, then write the val...

    Text Solution

    |

  6. Write the value of the following determinant abs{:(a-b, b-c, c-a),(b-c...

    Text Solution

    |

  7. Use properties of determinants ot evaluate: {:|(2,a,abc),(2,b,bca),(...

    Text Solution

    |

  8. Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y)...

    Text Solution

    |

  9. Evaluate |[102,18,36],[1,3,4],[17,3,6]|

    Text Solution

    |

  10. Use properties of determinants ot evaluate: {:|(2,3,1),(4,6,2),(1,3,...

    Text Solution

    |

  11. Use properties of determinants ot evaluate: {:|(2,3,5),(261,592,127)...

    Text Solution

    |

  12. Show that x=1 is a root of the equation: {:|(x+1,2x,-11),(2x,x+1,-4...

    Text Solution

    |

  13. If p,q,r ar in A.P. write the value of : {:|(x+1,x+2,x+2p),(x+2,x+3,...

    Text Solution

    |

  14. Without expanding, prove that the following determinant vanishes. |...

    Text Solution

    |

  15. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  16. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  17. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  18. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  19. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  20. Without expanding, prove that Delta = abs{:(x+y, y + z, z+ x),(z, x ,...

    Text Solution

    |

  21. Without expanding, prove that : |{:(1, bc, a(b+ c) ),(1, ca, b ( c+ a)...

    Text Solution

    |