Home
Class 12
MATHS
If A is a diagonal matrix of order 3xx3 ...

If `A` is a diagonal matrix of order `3xx3` is commutative with every square matrix or order `3xx3` under multiplication and `t r(A)=12 ,` then the value of `|A|^(1//2)` is ______.

Text Solution

Verified by Experts

The correct Answer is:
64
A diagonal matrix is commutative with every square matrix if it is scalar matrix, so every diagonal element is 4. Therefore,
`|A|=64`
Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

Let A be a square matrix of order 3 such that det. (A)=1/3 , then the value of det. ("adj. "A^(-1)) is

If A is an ivertible matrix of order 3xx3 and |A| = 6, then find the value of |adj.A|.

Let A be a square matrix of order 3xx3 , then |KA| is equal to

Find co-factor of a_(31) for a matrix of order 3xx3

If A is an invertible matrix of order 3 and |A| =5, then the value of |adjA| is equal to

If A is a square matrix of order 3xx3 and lambda is a scalar, then adj (lambdaA) is equal to -

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

If I is the unit matrix of order 10xx10 , then the determinant of I is equal to -

Let A be a nonsingular square matrix of order 3xx3 .Then |adj A| is equal to

If one of the eigenvalues of a square matrix a order 3xx3 is zero, then prove that det A=0 .

CENGAGE PUBLICATION-MATRICES-All Questions
  1. Let A=([a(i j)])(3xx3) be a matrix such that AA^T=4Ia n da(i j)+2c(i j...

    Text Solution

    |

  2. Let S be the set which contains all possible values of l ,m ,n ,p ,q ,...

    Text Solution

    |

  3. If A is a diagonal matrix of order 3xx3 is commutative with every squa...

    Text Solution

    |

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

    Text Solution

    |

  5. If A and B are two matrices of order 3 such that AB=O and A^(2)+B=I, t...

    Text Solution

    |

  6. If a, b, and c are integers, then number of matrices A=[(a,b,c),(b,c,a...

    Text Solution

    |

  7. Let A=[a("ij")] be 3xx3 matrix and B=[b("ij")] be 3xx3 matrix such tha...

    Text Solution

    |

  8. A square matrix M of order 3 satisfies M^(2)=I-M, where I is an identi...

    Text Solution

    |

  9. Let A=[a("ij")](3xx3), B=[b("ij")](3xx3) and C=[c("ij")](3xx3) be any ...

    Text Solution

    |

  10. If A is a square matrix of order 2xx2 such that |A|=27, then sum of th...

    Text Solution

    |

  11. If A is a square matrix of order 2 and det. A=10, then ((tr. A)^(2)-tr...

    Text Solution

    |

  12. Let A and B are two square matrices of order 3 such that det. (A)=3 an...

    Text Solution

    |

  13. Let P, Q and R be invertible matrices of order 3 such A=PQ^(-1), B=QR^...

    Text Solution

    |

  14. If P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of a 3xx3 matrix A a...

    Text Solution

    |

  15. A, B and C are three square matrices of order 3 such that A= diag (x, ...

    Text Solution

    |

  16. Let A=[a("ij")] be a matrix of order 2 where a("ij") in {-1, 0, 1} and...

    Text Solution

    |

  17. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

    Text Solution

    |

  18. The number of 3 x 3 non-singular matrices, with four entries as 1 and ...

    Text Solution

    |

  19. Let A be a 2 xx 2 matrix with non-zero entries and let A^2=I, where i ...

    Text Solution

    |

  20. Let A and B two symmetric matrices of order 3. Statement 1 : A(BA) a...

    Text Solution

    |