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

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

A

0

B

`A^(2)+B^(2)`

C

`A^(2)+2AB+B^(2)`

D

`A+B`

Text Solution

Verified by Experts

The correct Answer is:
B
`:'B=-A^(-1)BA`
`impliesAB=-("AA"^(-1))BA`
(Pre multiplying both sides of A)
`impliesAB=-lBAimpliesAB=-BA`
Now `(A+B)^(2)=(A+B)(A+B)`
`=A^(2)+AB+BA+B^(2)`
`=A^(2)-BA+BA+B^(2)=A^(2)+B^(2)`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|18 Videos

  • MATRICES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|18 Videos

  • MATHEMATICAL LOGIC

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|22 Videos

  • MHTCET 2007

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MATHEMATICS|50 Videos

Similar Questions

Explore conceptually related problems

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 such that AB=A and BA=B , then A^(2) equals

If A and B are square matrices of the same order such that B=-A^(-1)BA, then (A+B)^(2)

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

If A and B are square matrices of same order such as AB=A,BA=B then (A+I)^(5) is equal to (where I is the unit matrix):-

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 matrices such that AB=B and BA=A, then

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

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MATRICES-MISCELLANEOUS PROBLEMS
  1. If B is a non-singular matrix and A is a square matrix, then det (B^(-...

    Text Solution

    |

  2. If a matrix A is such that 3A^3 +2A^2+5A+I= 0, then A^(-1) is equal to

    Text Solution

    |

  3. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)^(...

    Text Solution

    |

  4. If A is a non -singular matrix such that A^(3)=A+l, then the inverse o...

    Text Solution

    |

  5. If A is a skew symmetric matrix of order n and C is a column matrix of...

    Text Solution

    |

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

    Text Solution

    |

  7. Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the fo...

    Text Solution

    |

  8. If A is a non-singular matrix of order 3, then adj(adj(A)) is equal to

    Text Solution

    |

  9. Let {:A=[(1,2),(-5,1)]and A^(-1)=xA+yI:}, then the values of x and y a...

    Text Solution

    |

  10. Let A =[(1,-1,1),(2,1,-3),(1,1,1)] and 10B=[(4,2,2),(-5,0,alpha),(...

    Text Solution

    |

  11. If A(theta)=[(1, than theta),(-tan, theta=1)] and AB=l, then (sec^(2)t...

    Text Solution

    |

  12. If A=[(cos alpha, -sin alpha, 0),(sin alpha, cos alpha,0),(0,0,1)] the...

    Text Solution

    |

  13. Suppose A is a matrix of order 3 and B=|A|A^(-1). If |A|=5, then |B| i...

    Text Solution

    |

  14. if[{:(2,1),(3,2):}]A[{:(-3,2),(5,-3):}]=[{:(1,0),(0,1):}],"then" A=?

    Text Solution

    |

  15. If f(theta)=[(cos theta, -sin theta,0),(sin theta, cos theta, 0),(0,0,...

    Text Solution

    |

  16. If A is a singular matrix, then Aadj(A) is a/an

    Text Solution

    |

  17. If k is a scalar and l is a unit matrix of order 3 then adj(kl) is equ...

    Text Solution

    |

  18. Consider the system of equations x+y+z=6 x+2y+3z=10 x+2y+lambda...

    Text Solution

    |

  19. Let a, b, c be any real numbers. Suppose that there are real numbers...

    Text Solution

    |

  20. Let a, b, c be positive real numbers. The following system of equation...

    Text Solution

    |