Home
Class 12
MATHS
If A and B are two matrices such th...

If `A` and `B` are two matrices such that `A B=A` and `B A=B` , then `B^2` is equal to (a) `B` (b) `A` (c) 1 (d) 0

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the given conditions involving matrices \( A \) and \( B \): 1. **Given Conditions**: - \( AB = A \) (Equation 1) - \( BA = B \) (Equation 2) 2. **Objective**: - We want to find \( B^2 \). ...
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos
  • ALGEBRA OF VECTORS

    RD SHARMA|Exercise Solved Examples And Exercises|331 Videos

Similar Questions

Explore conceptually related problems

If A and B are two matrices such that A+B =AB , then

if A and B are two matrices such that AB=B and BA=A,then A^(2)+B^(2) is equal to

If A and B are two square matrices such that AB=A and BA=B , then A^(2) equals

If A and B are two matrices such that AB=B and BA=A, then A^(2)+B^(2)=

If A and B are two matrices such that AB=A, BA=B, then A^25 is equal to (A) A^-1 (B) A (C) B^-1 (D) B

If A and B are two square matrices such that B=-A^(-1)BA , then (A+B)^(2) is equal to

If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)^(2) is eual to-

If A and B are two square matrices of same order satisfying AB=A and BA=B, then B^2 is equal to A (B) B (C) A^2 (D) none of these

If A and B are two matrices such that AB=B and BA=A then A^2+B^2= (A) 2AB (B) 2BA (C) A+B (D) AB

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A=[(1 ,0, 0),(0, 1,0),( a,b, -1)] , then A^2 is equal to (a) a n...

    Text Solution

    |

  2. If A=[i0 0i],\ n in N , then A^(4n) equals [0i i0] (b) [0 0 0 0] (c) ...

    Text Solution

    |

  3. If A and B are two matrices such that A B=A and B A=B , then B^...

    Text Solution

    |

  4. If A B=A and B A=B , where A and B are square matrices, then B^2=B ...

    Text Solution

    |

  5. If A and B are two matrices such that AB=B and BA=A , then A^2+B^2=

    Text Solution

    |

  6. If [(cos\ (2pi)/7,-sin\ (2pi)/7),(sin\ (2pi)/7,cos\ (2pi)/7)]^k=[(1,0)...

    Text Solution

    |

  7. If the matrix A B is zero, then It is not necessary that either A=O...

    Text Solution

    |

  8. Let A=[(a,0, 0),( 0,a,0),( 0, 0,a)] , then A^n is equal to [(a^n,0,...

    Text Solution

    |

  9. If A ,\ B are square matrices of order 3,\ A is non-singular and A ...

    Text Solution

    |

  10. If A=[(n,0 ,0),( 0,n,0),( 0, 0,n)] and B=[(a1,a2,a3),(b1,b2,b3),(c1,c2...

    Text Solution

    |

  11. If A=[(1,a),(0, 1)] , then A^n (where n in N) equals [(1,n a),(0,...

    Text Solution

    |

  12. If A=[1 2x0 1 0 0 0 1] and B=[1-2y0 1 0 0 0 1] and A B=I3 , then x+y e...

    Text Solution

    |

  13. If A=[1-1 2-1] , B=[a1b-1] and (A+B)^2=A^2+B^2 , then values of a and ...

    Text Solution

    |

  14. If A=[alphabetagamma-alpha] is such that A^2=I , then 1+alpha^2+betaga...

    Text Solution

    |

  15. If S=[S(i j)] is a scalar matrix such that s(i i)=ka n dA is a square ...

    Text Solution

    |

  16. If a square matrix such that A^2=A , then (I+A)^3-7A is equal to A ...

    Text Solution

    |

  17. If a matrix A is both symmetric and skew-symmetric, then A is a

    Text Solution

    |

  18. The matrix [(0, 5,-7),(-5, 0, 11),( 7,-11, 0)] is (a) a skew-symmetr...

    Text Solution

    |

  19. If A is a square matrix, then A A is a (a) skew-symmetric matrix (b)...

    Text Solution

    |

  20. If A and B are symmetric matrices, then A B A is (a) symmetric m...

    Text Solution

    |