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An orthogonal matrix is...

An orthogonal matrix is

A

`[(cos alpha, 2 sin alpha),(-2 sin alpha, cos alpha)]`

B

`[(cos alpha, sin alpha),(- sin alpha, cos alpha)]`

C

`[(cos alpha, sin alpha),(sin alpha, cos alpha)]`

D

`[(1,1),(1,1)]`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • The determinant of a orthogonal matrix is

    A
    `+-1`
    B
    2
    C
    0
    D
    `+-2`

  • The determinant of a orthogonal matrix is :

    A
    `+- 1`
    B
    2
    C
    0
    D
    `+- 2`

  • Let the matrices A=[{:( sqrt3,-2),(0,1):}] and P be any orthogonal matrix such that Q = PAP and let Rne [r_0] _(2-2)=P'Q^(6) P then

    A
    `r_(11) =81 `
    B
    `r_(1l) =81 sqrt3`
    C
    ` r_(11) -4sqrt3`
    D
    ` r_(11)=-sqrt3`

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    A square matrix A is said to be orthogonal if A^T A=I If A is a sqaure matrix of order n and k is a scalar, then |kA|=K^n |A| Also |A^T|=|A| and for any two square matrix A d B of same order \AB|=|A||B| On the basis of abov einformation answer the following question: If A is an orthogonal matrix then (A) A^T is an orthogonal matrix but A^-1 is not an orthogonal matrix (B) A^T is not an orthogonal mastrix but A^-1 is an orthogonal matrix (C) Neither A^T nor A^-1 is an orthogonal matrix (D) Both A^T and A^-1 are orthogonal matices.

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