Home
Class 12
MATHS
If A is a square matrix such that |A|=2 ...

If `A` is a square matrix such that `|A|=2` , write the value of `|AA^T|`

Text Solution

Verified by Experts

Given that `|A| = 2`, we have to find `| A A^T|`
Using `|AB| = |A||B| `and `|A^T| = |A|,`
we get` |A A^T| = |A||A^T|`
= `|A||A| = 2 xx 2 = 4`
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos
  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos

Similar Questions

Explore conceptually related problems

If A is a square matrix such that |A|=2 write the value of |AA^(T)|

If A is a square matrix of order 3 such that |A|=5 , write the value of |a d j\ A| .

If A is a square matrix such that A^(2)=A then write the value of 7A-(I+A)^(3), where I is the identity matrix.

If A is a square matrix of order 3 such that |A|=2, then write the value of adj(adjA)

If A is a square matrix and |A|=2, then write the value of |AA'|, where A' is the transpose of matrix A

If A is an square matrix of order 3 such that |A|=2, then write the value of |adj(adjA)|

If A is a square matrix of order 3 with |AI=2, then the value of |(A-A^(T))^(5)|+|(A-A^(T))^(3)| is

If A is a square matrix with |A|=8 , then find the value of |A A'| .

If A is a square matrix such that A^(3) =I then the value of A^(-1) is equal to

If A is a square matrix of order 3 with |A|=9 , then write the value of |2.adj.A| .

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. A is a skew-symmetric of order 3, write the value of |A| .

    Text Solution

    |

  2. If A is a square matrix of order 3 with determinant 4, then write t...

    Text Solution

    |

  3. If A is a square matrix such that |A|=2 , write the value of |AA^T|

    Text Solution

    |

  4. Find the value of determinant |243 156 300 81 52 100-3 0 4| .

    Text Solution

    |

  5. Write the value of the determinant |2-3 5 4-6 10 6-9 15| .

    Text Solution

    |

  6. If the matrix [5x2-10 1] is singular, find the value of x .

    Text Solution

    |

  7. If A is a square matrix of order nxxn such that |A|=lambda , then w...

    Text Solution

    |

  8. Find the value of the determinant |2^2 2^3 2^4 2^3 2^4 2^5 2^4 2^5 ...

    Text Solution

    |

  9. If A and B are non-singular matrices of the same order, write wheth...

    Text Solution

    |

  10. A matrix of order 3xx3 has determinant 2. What is the value of |A(3...

    Text Solution

    |

  11. If A and B are square matrices of order 3 such that |A|=-1 , |B|=3 ...

    Text Solution

    |

  12. Write the value of |a+i b c+i d-c+i d a-i b| .

    Text Solution

    |

  13. Write the cofactor of a(12) in the matrix [2-3 5 6 0 4 1 5-7]

    Text Solution

    |

  14. If |[2x+5, 3], [5x+2, 9]|=0 , find xdot

    Text Solution

    |

  15. Find the value of x from the following: |[x,4], [2, 2x]|=0

    Text Solution

    |

  16. Write the value of the determinant |A|=|[2,3,4],[5,6,8],[6x,9x,12x]|

    Text Solution

    |

  17. If |A|=2 , where A is 2xx2 matrix, find |a d j\ A| .

    Text Solution

    |

  18. What is the value of the determinant |[0, 2, 0],[ 2, 3, 4],[ 4 ,5 ,...

    Text Solution

    |

  19. For what value of x is the matrix[[6-x,4 ],[3-x,1]] singular?

    Text Solution

    |

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

    Text Solution

    |