Home
Class 12
MATHS
If A is an 3xx3 non-singular matrix such...

If A is an `3xx3` non-singular matrix such that `A A^T=A^TA and B=A^(-1)A^T," then " B B^T` equals

A

`B^(-1)`

B

`(B^(-1))`

C

`I+B`

D

`I`

Text Solution

Verified by Experts

The correct Answer is:
D
`B = A^(-1) A'`
`B' = (A ^(-1) A')' = A(A^(-1))'`
Now, `BB' = (A^(-1)A') A(A^(-1)) ' = A^(-1) (A'A) (A^(-1))'`
`= A^(-1) (A A')(A^(-1)) " " [because A' A = A A' ]`
`= (A^(-1) A) A'(A^(-1))'`
`= (IA') (A^(-1))'=A^'(A^(-1))' = (A^(-1)A) ' = I' = I`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|14 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

If A is an 3xx3 non-singular matrix such that A A^' = A^' A and B""=""A^(-1)A^' , then BB^' equals (1) I""+""B (2) I (3) B^(-1) (4) (B^(-1))^'

If A is a 3 xx 3 non-singular matrix such that A A^(T) = A^(T)A " and "B = A^(-1)A^(T), " then "B B^(T) is equal to

If A is a nonsingular matrix such that A A^(T)=A^(T)A and B=A^(-1) A^(T) , then matrix B is

If A is a non-singular matrix such that AA^(T)=A^(T)A and B=A^(-1)A^(T), the matrix B is a.involuntary b.orthogonal c.idempotent d. none of these

If A is an 3xx3 non-singular matrix such that A A^(prime)=A^(prime)A a n dB=A^(-1)A^(prime), then B B ' equals: (a) B^(-1) (b) (B^(-1))' (c) I+B (d) I

If A is a square matrix such that A A^T=I=A^TA , then A is

If A is a 3xx3 non-singular matrix,then |A^(-1)adj(A)| is

ARIHANT MATHS-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

    Text Solution

    |

  2. Let A and B are symmetric matrices of order 3. Statement -1 A (BA) a...

    Text Solution

    |

  3. Let P = [a(ij)] " be a " 3 xx 3 matrix and let Q = [b(ij)], " where " ...

    Text Solution

    |

  4. If P is a 3xx3 matrix such that P^T = 2P+I, where P^T is the transpose...

    Text Solution

    |

  5. If the adjoint of a 3 3 matrix P is 1 4 4 2 1 7 1 1 3 , then the po...

    Text Solution

    |

  6. If A =((1,0,0),(2,1,0),(3,2,1)) u(1) and u(2) are the column matrices ...

    Text Solution

    |

  7. Let P and Q be 3xx3 matrices with P!=Q . If P^3=""Q^3a n d""P^2Q""=""Q...

    Text Solution

    |

  8. If P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of a 3 x 3 matrix ...

    Text Solution

    |

  9. For 3xx3 matrices Ma n dN , which of the following statement (s) is (a...

    Text Solution

    |

  10. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

    Text Solution

    |

  11. If A is an 3xx3 non-singular matrix such that A A^T=A^TA and B=A^(-1)A...

    Text Solution

    |

  12. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

    Text Solution

    |

  13. Let m and N be two 3x3 matrices such that MN=NM. Further if M!=N^2 and...

    Text Solution

    |

  14. If A=[1 2 2 2 1-2a2b] is a matrix satisfying the equation AA^T=""9I , ...

    Text Solution

    |

  15. Let Xa n dY be two arbitrary, 3xx3 , non-zero, skew-symmetric matrices...

    Text Solution

    |

  16. If A=[5a-b3 2] and A adj A=AA^T , then 5a+b is equal to: (1) -1 (2) ...

    Text Solution

    |

  17. Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[...

    Text Solution

    |

  18. let z= (-1+sqrt(3i))/2, where i=sqrt(-1) and r,s epsilon P1,2,3}. Let ...

    Text Solution

    |

  19. Let P=[[1,0,0],[4,1,0],[16,4,1]]and I be the identity matrix of order ...

    Text Solution

    |

  20. if A=[[2,-3],[-4,1]] then (3A^2+12A)=?

    Text Solution

    |