Home
Class 12
MATHS
If S is a real skew-symmetric matrix, ...

If `S` is a real skew-symmetric matrix, then prove that `I-S` is non-singular and the matrix `A=(I+S)(I-S)^(-1)` is orthogonal.

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

If A and B are symmetric matrices, prove that AB-BA is a skew symmetric matrix.

If A is a 3xx3 skew-symmetric matrix, then trace of A is equal to -1 b. 1 c. |A| d. none of these

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

If A is a symmetric matrix, B is a skew-symmetric matrix, A+B is nonsingular and C=(A+B)^(-1) (A-B) , then prove that (i) C^(T) (A+B) C=A+B (ii) C^(T) (A-B)C=A-B (iii) C^(T)AC=A

If A is a skew symmetric matrix, then B=(I-A)(I+A)^(-1) is (where I is an identity matrix of same order as of A )

A skew-symmetric matrix A satisfies the relation A^2+I=O ,w h e r e , I is a unit matrix then A is a. idempotent b. orthogonal c. of even order d. odd order

If A and B are non-singular symmetric matrices such that AB=BA , then prove that A^(-1) B^(-1) is symmetric matrix.

What is the S.I. unit of heat

In the set all 3xx 3 real matric a relation a relation is defined as follows .A matrix A is related to a matric B if and only if there is a non - singular 3xx 3 matrix P such that B=P^(-1) AP. This relation is -

If A is non-diagonal involuntary matrix, then a. A-I=O b. A+I=O c. A-I is nonzero singular d. none of these

CENGAGE PUBLICATION-MATRICES-All Questions
  1. If B ,C are square matrices of order na n difA=B+C ,B C=C B ,C^2=O , ...

    Text Solution

    |

  2. Statement 1: if D=diag[d1, d2, ,dn],then D^(-1)=diag[d1^(-1),d2^(-1),...

    Text Solution

    |

  3. If S is a real skew-symmetric matrix, then prove that I-S is non-si...

    Text Solution

    |

  4. If B and C are non-singular matrices and O is null matrix, then show t...

    Text Solution

    |

  5. Find the possible square roots of the two rowed unit matrix I.

    Text Solution

    |

  6. If A=\begin{bmatrix} 1 & 2 & 2\\ 2 & 1 & 2\\ 2 & 2 & 1 \end{bmatrix} ,...

    Text Solution

    |

  7. Let M be a 3xx3 matrix satisfying M[[0], [1] ,[0]]=[[-1], [2], [3]]...

    Text Solution

    |

  8. If A is unimodular, then which of the following is unimodular? a. -A ...

    Text Solution

    |

  9. Consider three matrices A=[(2,1),(4,1)], B=[(3,4),(2,3)] and C=[(3,-4)...

    Text Solution

    |

  10. If A B=Aa n dB A=B , then which of the following is/are true? A is ide...

    Text Solution

    |

  11. If A=[[1,-1],[ 2, 1]],B=[[a,1],[b,-1]]a n d(A+B)^2=A^2+B^2+2A B ,t h e...

    Text Solution

    |

  12. Let Aa n dB be two nonsingular square matrices, A^T a n dB^T are the t...

    Text Solution

    |

  13. If A=1/3|[1, 2, 2], [2, 1,-2],[a,2,b]| is an orthogonal matrix, then ...

    Text Solution

    |

  14. If A is a matrix such that A^2+A+2I=Odot, the which of the following i...

    Text Solution

    |

  15. If A(theta)=[[sintheta, icostheta], [icostheta, sintheta]] , then whic...

    Text Solution

    |

  16. If |(1,-t a ntheta),(t a ntheta,1)| |(1,t a ntheta),(-t a ntheta,1)|^-...

    Text Solution

    |

  17. If A=[[3,-3, 4], [2,-3, 4], [0,-1, 1]] , then a. a d j(a d j A)=A b. |...

    Text Solution

    |

  18. If [[alpha, beta], [gamma, -alpha]] is to be square root of two-rowed ...

    Text Solution

    |

  19. If A=[a("ij")](4xx4), such that a("ij")={(2",","when "i=j),(0",","when...

    Text Solution

    |

  20. Statement 1: Let A ,B be two square matrices of the same order such th...

    Text Solution

    |