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If A = [{:("cos" theta, -"sin"theta),("s...

If `A = [{:("cos" theta, -"sin"theta),("sin"theta, "cos"theta):}]`, then the matrix `A^(-50) " when " theta = (pi)/(12)`, is equal to

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Knowledge Check

  • If A=[(costheta, -sin theta ),(sin theta, cos theta) ] , then the matrix A^(-50) when theta=pi/12 , is equal to :

    A
    `[(1/2,sqrt3,2),(-sqrt3/2, 1/2)]`
    B
    `[(sqrt3/2, -1/2),(1/2,sqrt3/2)]`
    C
    `[(sqrt3/2,1/2),(-1/2, sqrt3/2)]`
    D
    `[(1/2, -sqrt3/2),(sqrt3/2,1/2)]`

  • Inverse of the matrix [{:(cos 2 theta, -sin 2 theta),(sin 2 theta, cos 2 theta):}] is

    A
    `[{:(cos 2 theta, -sin 2 theta),(sin 2 theta, cos 2 theta):}]`
    B
    `[{:(cos 2 theta, sin 2 theta),(sin 2 theta, -cos 2 theta):}]`
    C
    `[{:(cos 2 theta, sin 2 theta),(sin 2 theta, cos 2 theta):}]`
    D
    `[{:(cos 2 theta, sin 2 theta),(-sin 2 theta, cos 2 theta):}]`

  • cos theta [(cos theta, sin theta),(-sin theta, cos theta)]+sin theta[(sin theta, -cos theta),(cos theta, sin theta)] is equal to

    A
    `[(1,0),(0,1)]`
    B
    `[(0,1),(1,0)]`
    C
    `[(0,0),(1,1)]`
    D
    None of these

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