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

`A` and `B` are two square matrices such that `A^(2)B=BA` and if `(AB)^(10)=A^(k)B^(10)`, then `k` is

A

`1001`

B

`1023`

C

`1042`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `(AB).(AB)=A(BA)B`
`=A^(3)B^(2)`
`(AB)(AB)(AB)=A^(7)B^(3)`
so `(AB)^(n)=A^(z^(n-1))B^(n)`
so `k=2^(10)=1=1023`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Multiple Correct Answer|7 Videos

  • MATRICES

    CENGAGE|Exercise JEE Advanced Previous Year|26 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 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 equal to

A and B be 3xx3 matrices such that AB+A=0 , then

Let A and B be two non-singular square matrices such that B ne I and AB^(2)=BA . If A^(3)-B^(-1)A^(3)B^(n) , then value of n is

If A and B are square matrices such that AB = BA then prove that A^(3)-B^(3)=(A-B) (A^(2)+AB+B^(2)) .

if A and B are two matrices of order 3xx3 so that AB=A and BA=B then (A+B)^7=

Let A and B are two square matrices of order 3 such that det. (A)=3 and det. (B)=2 , then the value of det. (("adj. "(B^(-1) A^(-1)))^(-1)) is equal to _______ .

If A and B are two square matrices of order 3xx3 which satify AB=A and BA=B , then (A+I)^(5) is equal to (where I is idensity matric)

If A and B are two non-singular matrices which commute, then (A(A+B)^(-1)B)^(-1)(AB)=

CENGAGE-MATRICES-Single correct Answer
  1. If the value of prod(k=1)^(50)[{:(1,2k-1),(0,1):}] is equal to [{:(1,r...

    Text Solution

    |

  2. A square matrix P satisfies P^(2)=I-P where I is identity matrix. If P...

    Text Solution

    |

  3. A and B are two square matrices such that A^(2)B=BA and if (AB)^(10)=A...

    Text Solution

    |

  4. If matrix A=[a(ij)](3xx), matrix B=[b(ij)](3xx3), where a(ij)+a(ji)=0 ...

    Text Solution

    |

  5. If A({:(1,3,4),(3,-1,5),(-2,4,-3):})=({:(3,-1,5),(1,3,4),(+4,-8,6):}),...

    Text Solution

    |

  6. Let A=[{:(-5,-8,-7),(3,5,4),(2,3,3):}] and B=[{:(x),(y),(1):}]. If AB ...

    Text Solution

    |

  7. A=[{:(a,b),(b,-a):}] and MA=A^(2m), m in N for some matrix M, then whi...

    Text Solution

    |

  8. If A=[a(ij)](mxxn) and a(ij)=(i^(2)+j^(2)-ij)(j-i), n odd, then which ...

    Text Solution

    |

  9. |A-B| ne 0, A^(4)=B^(4), C^(3)A=C^(3)B, B^(3)A=A^(3)B, then |A^(3)+B^(...

    Text Solution

    |

  10. If AB+BA=0, then which of the following is equivalent to A^(3)-B^(3)

    Text Solution

    |

  11. A,B,C are three matrices of the same order such that any two are symme...

    Text Solution

    |

  12. If A and P are different matrices of order n satisfying A^(3)=P^(3) an...

    Text Solution

    |

  13. Let A, B are square matrices of same order satisfying AB=A and BA=B th...

    Text Solution

    |

  14. The number of 2xx2 matrices A, that are there with the elements as rea...

    Text Solution

    |

  15. If the orthogonal square matrices A and B of same size satisfy detA+de...

    Text Solution

    |

  16. If A=[{:(costheta,sintheta),(sintheta,-costheta):}], B=[{:(1,0),(-1,1)...

    Text Solution

    |

  17. Let A be a 3xx3 matrix given by A=(a(ij))(3xx3). If for every column v...

    Text Solution

    |

  18. Suppose A and B are two non singular matrices such that B != I, A^6 = ...

    Text Solution

    |

  19. Let A be a 2xx3 matrix, whereas B be a 3xx2 amtrix. If det.(AB)=4, the...

    Text Solution

    |

  20. Let A be a square matrix of order 3 so that sum of elements of each ro...

    Text Solution

    |