Home
Class 12
MATHS
Prove that inverse of a skew-symmetric m...

Prove that inverse of a skew-symmetric matrix (if it exists) is skew-symmetric.

Text Solution

Verified by Experts

A is skew-symmetric, then `A^(T)=-A`.
`:. (A^(-1))^(T)=(A^(T))^(-1)=(-A)^(-1) =-A^(-1)`
Thus, `A^(-1)` is skew-symmetric.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise (Single)|65 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Multiple)|33 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.4|12 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

The inverse of a skew symmetric matrix is

The inverse of a skew-symmetric matrix of odd order a.is a symmetric matrix b.is a skew- symmetric c.is a diagonal matrix d.does not exist

Let A be a square matrix.Then prove that (i)A+A^(T) is a symmetric matrix,(ii) A-A^(T) is a skew-symmetric matrix and (iii)AA^(T) and A^(T)A are symmetric matrices.

The inverse of a skew symmetric matrix of odd order is 1)a symmetric matrix 2)a skew symmetric matrix 3)a diagonal matrix 4)does not exist

Show that positive odd integral powers of a skew-symmetric matrix are skew-symmetric and positive even integral powers of a skew- symmetric matrix are symmetric.

If A is skew-symmetric matrix then A^(2) is a symmetric matrix.

A square matrix A is said skew - symmetric matrix if

If A, B are square matrices of same order and B is skew-symmetric matrix, then show that A'BA is skew -symmetric.

Trace of a skew symmetric matrix is always equal to

CENGAGE-MATRICES-Exercise 13.5
  1. By the method of matrix inversion, solve the system. [(1,1,1),(2,5,7...

    Text Solution

    |

  2. Let A=[[2,0,7] , [0,1,0], [1,-2,1]] and B=[[-x,14x,7x] , [0,1,0] , [x,...

    Text Solution

    |

  3. Find A^(-1) if A=|(0,1,1),(1,0,1),(1,1,0)| and show that A^(-1)=(A^(2)...

    Text Solution

    |

  4. For the matrix A=[3 1 7 5] , find x and y so that A^2+x I=y Adot

    Text Solution

    |

  5. If A^(3)=O, then prove that (I-A)^(-1) =I+A+A^(2).

    Text Solution

    |

  6. If A=[[cos alpha, -sin alpha] , [sin alpha, cos alpha]], B=[[cos2beta,...

    Text Solution

    |

  7. If A=[(1,2,2),(2,2,3),(1,-1,3)], C=[(2,1,1),(2,2,1),(1,1,1)], D=[(10),...

    Text Solution

    |

  8. If A is a 2xx2 matrix such that A^(2)-4A+3I=O, then prove that (A+3I)^...

    Text Solution

    |

  9. For two unimobular complex numbers z(1) and z(2), find [(bar(z)(1),-z(...

    Text Solution

    |

  10. Prove that inverse of a skew-symmetric matrix (if it exists) is skew-s...

    Text Solution

    |

  11. If square matrix a is orthogonal, then prove that its inverse is also ...

    Text Solution

    |

  12. If A is a skew symmetric matrix, then B=(I-A)(I+A)^(-1) is (where I is...

    Text Solution

    |

  13. Prove that ("adj. "A)^(-1)=("adj. "A^(-1)).

    Text Solution

    |

  14. Using elementary transformation, find the inverse of the matrix A=[(a,...

    Text Solution

    |

  15. Show that the two matrices A, P^(-1) AP have the same characteristic r...

    Text Solution

    |

  16. Show that the characteristics roots of an idempotent matris are either...

    Text Solution

    |

  17. If alpha is a characteristic root of a nonsin-gular matrix, then prove...

    Text Solution

    |