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 of order `3xx3` under multiplication and trace (A)=12, then find |A|

Text Solution

Verified by Experts

The correct Answer is:
64
Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise EXERCISE-2|19 Videos

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise PART-III|18 Videos

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise SECTION-D|17 Videos

  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise SELF PRACTIC PROBLEMS|25 Videos

  • NUMBER THEORY

    RESONANCE ENGLISH|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

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 ______.

If A is a matrix of order 3, then det(kA) is

If A is a matrix of order 3xx3 , then |3A| is equal to………

If A is any square matrix of order 3xx3 such that |A|=3, then the value of |adjA| is ?

A matrix A of order 3xx3 is such that |A|=4 . Find the value of |2A| .

If A is invertible matrix of order 3xx3 , then |A^(-1)| is equal to…………

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

If A is a matrix of order 3xx4 and B is a matrix of order 4xx3 , find the order of the matrix of A Bdot

RESONANCE ENGLISH-MATRICES & DETERMINANT-PART-II
  1. Let A=[{:p q q p:}] such that det(A)=r where p,q,r all prime number, t...

    Text Solution

    |

  2. Let A=[(0,1),(2,0)] and (A^(8)+A^(6)+A^(2)+I)V=[(32),(62)] where I i...

    Text Solution

    |

  3. Let A=[3x^2 1 6x],B=[abc],a n dC=[(x+2)^2 5x^2 2x5x^2 2x(x+2)^2 2x(x+2...

    Text Solution

    |

  4. Let A be an involutary matrix and S be the set containing solution of ...

    Text Solution

    |

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

    Text Solution

    |

  6. A is a (3xx3) diagonal matrix having integral entries such that det (A...

    Text Solution

    |

  7. If a(1), a(2), a(3), 5, 4, a(6), a(7), a(8), a(9) are in H.P. and the ...

    Text Solution

    |

  8. If |{:(,a+b+2c,a,b),(,c,b+c+2a,b),(,c,a,c+a+2b):}|=k(alphaa+betab+gamm...

    Text Solution

    |

  9. If A is a square matrix of order 3 and A' denotes transpose of matrix ...

    Text Solution

    |

  10. Suppose A is a matrix such that A^2 =A and (I + A)^6 =I+ KA, then K is...

    Text Solution

    |

  11. |[-bc, b^2+bc, c^2 +bc],[a^2+ac,-ac,c^2+ac],[a^2+ab,b^2+ab,-ab]|=64. t...

    Text Solution

    |

  12. (i) Find maximum value of f(x)=|{:(1+sin^(2)x,cos^(2)x,4sin2x),(sin...

    Text Solution

    |

  13. If Delta(k) = |(k,1,5),(k^(2),2n +1,2n +1),(k^(3),3n^(2),3n +1)|, " th...

    Text Solution

    |

  14. The value of a for which system of equations , a^3x+(a+1)^3y+(a+2)^3z=...

    Text Solution

    |

  15. Consider the system linear equations in x ,y ,a n dz given by (s in3th...

    Text Solution

    |

  16. The value of k for which the set of equations 3x+ky-2z=0, x + ky + 3z ...

    Text Solution

    |

  17. A(1)=[a(1)] A(2)=[{:(,a(2),a(3)),(,a(4),a(5)):}] A(3)=[{:(,a(6),a(...

    Text Solution

    |

  18. If {1/2(A-A'+1)}^-1=2/lambda[(lambda-13,-lambda/3,lambda/3),(-17,10,-...

    Text Solution

    |

  19. Given A=[[2,0,-alpha],[5,alpha,0],[0,alpha,3]] For a in R-{a, b}, A^(-...

    Text Solution

    |

  20. Let a ,b , c be the real numbers. The following system of equations in...

    Text Solution

    |