Home
Class 12
MATHS
If A=[a(ij)](mxxn) and a(ij)=(i^(2)+j^(2...

If `A=[a_(ij)]_(mxxn)` and `a_(ij)=(i^(2)+j^(2)-ij)(j-i)`, `n` odd, then which of the following is not the value of `Tr(A)`

A

`0`

B

`|A|`

C

`2|A|`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` AS `a_(ij)=(i^(2)+j^(2)-ij)(j-i)`
`a_(ji)=(j^(2)+i^(2)-ji)(i-j)=-a_(ij)`
`impliesA` is skew symmetric `impliesT_(r )(A)=0`
Also `|A|=0`
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_(ij)=i^(2)-j and A=(a_(ij))_(2xx2) is:

A=[a_(ij)]_(mxxn) is a square matrix if …………

If A=(a_(ij))_(2xx2) .Where a_(ij) is given by (i-2j)^(2) then A is:

If a_(ij)=(1)/(2) (3i-2j) and A = [a_(ij)]_(2xx2) is

If (1+px+x^(2))^(n)=1+a_(1)x+a_(2)x^(2)+…+a_(2n)x^(2n) . Which of the following is true for 1 lt r lt 2n

Let A be the 2 xx 2 matrix given by A=[a_("ij")] where a_("ij") in {0, 1, 2, 3, 4} such theta a_(11)+a_(12)+a_(21)+a_(22)=4 then which of the following statement(s) is/are true ?

Statement 1: If A=([a_(i j)])_(nxxn) is such that ( a )_(i j)=a_(j i),AAi ,ja n dA^2=O , then matrix A null matrix. Statement 2: |A|=0.

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. |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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. If (A+B)^(2)=A^(2)+B^(2) and |A| ne 0 , then |B|= (where A and B are m...

    Text Solution

    |

  18. If A is a square matrix of order 3 such that |A|=5, then |Adj(4A)|=

    Text Solution

    |

  19. If A and B are symmetric and commute, then which of the following is/a...

    Text Solution

    |

  20. If A is a square matrix of order 3 such that |A|=2,t h e n|(a d jA^(-1...

    Text Solution

    |