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If A=[[costheta,sintheta],[-sintheta,cos...

If `A=[[costheta,sintheta],[-sintheta,costheta]]`, then prove that `A^n=[[cosntheta,sinntheta],[-sinntheta,cosntheta]], n in N`.

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Consider `A^2=[[costheta,sintheta],[-sintheta,costheta]].[[costheta,sintheta],[-sintheta,costheta]]`
`A ^ 2 =[ [ cos ^ 2 θ −sin ^ 2 ...
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Knowledge Check

  • If A=[[costheta, sintheta], [-sintheta, costheta]] , then |A^(-1)|=

    A
    `1`
    B
    `-1`
    C
    `2`
    D
    `4`

  • if A= [{:(costheta,sintheta),(-sintheta,costheta):}], then A A^T =?

    A
    `[{:(1,0),(0,1):}]`
    B
    `[{:(0,1),(1,0):}]`
    C
    `[{:(1,0),(0,-1):}]`
    D
    None of these

  • If A=[(costheta,-sintheta),(sintheta,costheta)] " then " A^(-1) =?

    A
    A
    B
    `-A`
    C
    adjA
    D
    `=-adjA`

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