Home
Class 12
MATHS
If A = [(1,0),(0,1)] and B = [(0,1),(-1,...

If `A = [(1,0),(0,1)] and B = [(0,1),(-1,0)]`, show that (pA + qB) (pA - qB) = `(p^2 + q^2)A`

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If A=[(2,-1),(0,1)] and B=[(1,0),(-1,-1)] then (A+B)^(2) is not equal to -

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

If A={:[(-2,1,3),(0,4,-1)]and B={:[(2,1),(-3,0),(4,-5)], show that, (AB)' = B'A' where A' is the transpose of A.

Let A = [(2,q),(0,1)] and A^(8) = [(x,yq),(0,1)], find x - y.

If A={:[(a,b),(c,d)] and I={:[(1,0),(0,1)] Show that, A^(2)-(a+d)A=(bc-ad)I .

If A = [{:(1,0,1),(0,1,2),(0,0,4):}] , then show that |3A|=27|A|.

If A={:[(1,-1,0),(-1,2,1),(0,1,1)]and B ={:[(1,1,-1),(0,1,-1),(0,0,1)] show that B^(T)AB is a diagonal matrix, where B^(T) is the transpose of B.

If A={:[(0,1,2),(1,2,3),(3,1,1)]and B={:[(2,1,3),(-1,0,1),(3,-1,4)], show that, AB ne BA .

If A={0,1} and B={0,-1} then show that AxxB ne BxxA

Prove that if A=[(1,0),(0,-1)] and B=[(0,1),(1,0)] , then AB=[(0,1),(-1,0)] . and BA=[(0,-1),(1,0)] . Clearly AB ne BA .

UNITED BOOK HOUSE-SET 18-EXERCISE
  1. If for two events A and B, P(A) = P(A/B) = 1/4 and P(B/A) = 1/2, show ...

    Text Solution

    |

  2. if tan ^(-1) x+tan ^(-1)y+tan ^(-1) z=pi/2 and x+y+z= sqrt3 , then sho...

    Text Solution

    |

  3. If A = [(1,0),(0,1)] and B = [(0,1),(-1,0)], show that (pA + qB) (pA -...

    Text Solution

    |

  4. If x,y,z are all distinct and if abs((x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^...

    Text Solution

    |

  5. Solve for x : |(x,a,b),(a,x,b),(a,b,x)| = 0

    Text Solution

    |

  6. Find the derivation of sin^-1 (x^2 sqrt(1-x) - sqrtx sqrt(1-x^4)) with...

    Text Solution

    |

  7. Evaluate : int(x^2dx)/((x sin x + cos x)^2)

    Text Solution

    |

  8. Solve: (dy)/(dx) +x(sin2y) = x^3 cos^2 y, y(0) = then y(1) equal to

    Text Solution

    |

  9. The temperature T of a cooling object drops at a rate proportional to ...

    Text Solution

    |

  10. If veca,vecb are unit vectors and theta be the angle between them show...

    Text Solution

    |

  11. If with reference to the right handed system of mutually perpendicular...

    Text Solution

    |

  12. Evaluate : underset(nrarrinfty)Lt[(1)/(sqrt(n^2 - 1^2)) + 1/(sqrt(n^...

    Text Solution

    |

  13. Evaluate : overset(log5)underset(0)int (e^xsqrt(e^x-1))/(e^x + 3 ) dx

    Text Solution

    |

  14. A random variable X has the following probability function: Calculate...

    Text Solution

    |

  15. A random variable X has the following probability function: Find P(x ...

    Text Solution

    |

  16. A random varible x has the following probability function: the va...

    Text Solution

    |

  17. Six coins are tossed at a time. Find the probability of occring not mo...

    Text Solution

    |

  18. In a certain culture the number of bacteria at any instant increases a...

    Text Solution

    |

  19. Find the equation of the common tangents to y^2 = 8ax and x^2 + y^2 = ...

    Text Solution

    |

  20. Prove that the radius of the right circular cylinder of greatest curve...

    Text Solution

    |