Home
Class 12
MATHS
Show that if A and B are square matrics ...

Show that if A and B are square matrics such that AB=BA , then `(A+B)^(2)=A^(2)+2AB+B^(2)`.

Text Solution

Verified by Experts

The correct Answer is:
`=A^(2)+2AB+B^(2)=R.H.S`.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Long Answer Type Questions)|4 Videos

  • MATRICES

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Objective type Questions)|15 Videos

  • MATRICES

    KUMAR PRAKASHAN|Exercise TEXTBOOK ILLUSTRATIONS FOR PRACTICE WORK |28 Videos

  • LINEAR PROGRAMMING

    KUMAR PRAKASHAN|Exercise PRACTICE WORK|25 Videos

  • PROBABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 13 (Section - D (Answer the following questions))|2 Videos

Similar Questions

Explore conceptually related problems

Statement -1 (Assertion) and Statement - 2 (Reason) Each of these examples also has four alternative choices, ONLY ONE of which is the correct answer. You have to select the correct choice as given below Statement-1 If A and B are two matrices such that AB = B, BA = A, then A^(2) + B^(2) = A+B. Statement-2 A and B are idempotent matrices, then A^(2) = A, B^(2) = B .

If A and B are two square matrices of the same order , then AB=Ba.

Let A and B are two matrices such that AB = BA, then for every n in N

If A and B are two matrices of the same order , then (AB) =A'B.

For square matrices A and B , AB=A and BA =B, then prove that A^(2)=AandB^(2)=B .

If A and B are square matrices of same order then (A^(-1)BA)^(n) = ………… , n inN .

Let A and B be square matrices of the order 3xx3 . Is (AB)^(2)=A^(2)B^(2) ? Given reasons .

If A and B are symmetric matrices of same order , then AB +BA is a ……

If A and B are square matrices of the same order such that AB=Ba , then prove by inducation that AB^(n)=B^(n)A . Further , prove that (AB)^(n)=A^(n)B^(n) for all n in N .

If AB=AandBA=B then A^(2)+B^(2)= ………..

KUMAR PRAKASHAN-MATRICES -Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. Show that A'A and A A ' are both symmetric matrices for any matrix A .

    Text Solution

    |

  2. Let A and B be square matrices of the order 3xx3 . Is (AB)^(2)=A^(2)B^...

    Text Solution

    |

  3. Show that if A and B are square matrics such that AB=BA , then (A+B)^(...

    Text Solution

    |

  4. Let A=[{:(1,2),(-1,3):}],B=[{:(4,0),(1,5):}],C=[{:(2,0),(1,-2):}]and a...

    Text Solution

    |

  5. If A=[{:(cosq,sinq),(-sinq,cosq):}] , then show that A^(2)=[{:(cos(2q...

    Text Solution

    |

  6. If A=[{:(0,-x),(x,0):}],B=[{:(0,1),(1,0):}]andx^(2)=-1 then show that ...

    Text Solution

    |

  7. Verify that A^(2)=I when A=[{:(0,1,-1),(4,-3,4),(3,-3,4):}].

    Text Solution

    |

  8. Prove by Mathematical Induction that (A)^(n)=(A^(n)) where n inN for a...

    Text Solution

    |

  9. Find inverse , by elementary row operations (if possible), of the foll...

    Text Solution

    |

  10. If [{:(xy,4),(z+6,x+y):}]=[{:(8,w),(0,6):}] , then find values of x,y,...

    Text Solution

    |

  11. If A=[{:(1,5),(7,12):}],B=[{:(9,1),(7,8):}] find a matrix C such that ...

    Text Solution

    |

  12. If A=[{:(3,-5),(-4,2):}], then find A^(2)-5A-14I. Hence , obtain A^(3)...

    Text Solution

    |

  13. Find the values of a,b ,c and d, if 3[{:(a,b),(c,d):}]=[{:(a,6),(-1,...

    Text Solution

    |

  14. Find the matrix X such that , [{:(2,-1),(1,0),(-3,4):}]X=[{:(-1,-8...

    Text Solution

    |

  15. If A=[{:(1,2),(4,1):}], find A^(2)+2A+7I.

    Text Solution

    |

  16. If A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}],andA^(-1)=A', find...

    Text Solution

    |

  17. If the maxtrix [{:(0,a,3),(2,b,-1),(c,1,0):}] is a skew symmetric mat...

    Text Solution

    |

  18. If p(x)=[{:(cosx,sinx),(-sinx,cosx):}] then show that p(x)*p(y)=p(x+y)...

    Text Solution

    |

  19. If A is square matrix such that A^(2)=A, show that (I+A)^(3)=7A+I.

    Text Solution

    |

  20. If A,B are square matrices of same order and B is a skew -symmetric ma...

    Text Solution

    |