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

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

Text Solution

Verified by Experts

Given: `A` and `B` are two matrices such that `AB=B` and `BA=A`
Then
`A^2+B^2=A``A+BB`
`A^2+B^2=A(BA)+B(AB)`
As `AB=B` and `BA=A`
`A^2+B^2=(AB)A+(BA)B`
`A^2+B^2=BA+AB`
`A^2+B^2=A+B`
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 3times3 matrices such that AB=A and BA=B, then

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 motrices, then A^(2) = A, B^(2) = B .

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=A and BA=B, then B^(2) is equal to (a) B( b) A(c)1(d)0

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

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 AB=BA then (A-B)^(2) =A^(2) - 2AB + B^(2) . True or False.

If, A and B be two matrices such that AB = A and BA=B. Then. Which of the following statements are correct ? 1. A^(2)=A 2. B^(2)=B 3. (AB)^(2)=AB

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

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

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A and B are two matrices such that A B=A and B A=B , then B^...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. If A=[(5,x),( y,0)] and A=A^T , then

    Text Solution

    |

  20. If A is 3xx4 matrix and B is a matrix such that A^T B and B A^T are bo...

    Text Solution

    |