Home
Class 12
MATHS
If A and B are square matrices of the sa...

If A and B are square matrices of the same order such that `A B=B A` , then show that `(A+B)^2=A^2+2A B+B^2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA ENGLISH|Exercise All Questions|181 Videos
  • ALGEBRA OF VECTORS

    RD SHARMA ENGLISH|Exercise All Questions|325 Videos

Similar Questions

Explore conceptually related problems

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

If A and B are any two square matrices of the same order than ,

If A and B arę square matrices of same order such that AB = A and BA = B, then

If A and B are square matrices of the same order such that AB=BA, then (A) (A-B)(A+B)=A^2-B^2 (B) (A+B)^2=A^2+2AB+B^2 (C) (A+B)^3=A^3A^2B+3AB^2+B^3 (D) (AB)^2=A^2B^2

If A and B are square matrices of order 3, then

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

If A and B are square matrices of same order such that AB=O and B ne O , then prove that |A|=0 .

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

If A and B are square matrices of the same order such that A=-B^(-1)AB then (A+3B)^(2) is equal to

If a and B are square matrices of same order such that AB+BA=O , then prove that A^(3)-B^(3)=(A+B) (A^(2)-AB-B^(2)) .

RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If S=[S(i j)] is a scalar matrix such that s(i i)= k and A is a square...

    Text Solution

    |

  2. If A is a square matrix, using mathematical induction prove that (A^T)...

    Text Solution

    |

  3. If A and B are square matrices of the same order such that A B=B A , t...

    Text Solution

    |

  4. There are 2 families A and B. There are 4 men, 6 women and 2 children ...

    Text Solution

    |

  5. If A={:[(-1),(2),(3)]:} and B=[-2" "-1" "-4] then verify that (AB)^(T)...

    Text Solution

    |

  6. If: [(xy,5x) , (z+6,y^2+1)]=[(8,w),(0,6)], then find the values of x ,...

    Text Solution

    |

  7. The sales figure of two car dealers during January 2013 showed that ...

    Text Solution

    |

  8. If A^T=[[3, 4],[-1, 2], [0 ,1]] and B=[[-1, 2, 1],[ 1, 2, 3]], find A^...

    Text Solution

    |

  9. If l1,""""m1,""""n1 and l2,""""m2,""""n2 are the direction cosines ...

    Text Solution

    |

  10. Construct a 2xx3 matrix A=[a(i j)] whose elements are given by a(i j)=...

    Text Solution

    |

  11. Construct a3×2m a t r i xA=[a(i j)] whose elements are given by a(i j...

    Text Solution

    |

  12. For what values of x and y such that matrices A and B are equal ? ...

    Text Solution

    |

  13. If [[x-y, z], [2x-y,omega]]=[[-1, 2], [4, 7]],then x , y , z ,omegado...

    Text Solution

    |

  14. Construct a 3×4m a t r i c A=[a(i j)] whose elements are given by a(i ...

    Text Solution

    |

  15. [[ x-y,2x+z] , [ 2x-y,3z+w ]] = [[ -1, 5 ] , [ 0, 13 ]], then ,x,y...

    Text Solution

    |

  16. Find the values of x , y , za n da which satisfy the matrix equation [...

    Text Solution

    |

  17. In a certain city there are 30 colleges. Each college has 15 peons, 6 ...

    Text Solution

    |

  18. If A=[(1,-1) ,(2 ,3)],B=[(2, 1), (1, 0)],p rove t h a t (A+B)^2!=A^2+...

    Text Solution

    |

  19. Find a matrix X such that 2A+B+X=0 , where A= [(-1, 2) ,(3, 4)],B=[(3,...

    Text Solution

    |

  20. If X and Y are 2xx2 matrices, then solve the following matrix equat...

    Text Solution

    |