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Matrices Question MEI

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    How do I go about this? The mark scheme on the MEI website confused me.

    Thanks,
    Sora
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    (Original post by Sora)
    Click image for larger version. 

Name:	Matrices.png 
Views:	52 
Size:	18.6 KB 
ID:	142262

    How do I go about this? The mark scheme on the MEI website confused me.

    Thanks,
    Sora
    Since A^3=I, what's A^{-1} in terms of A ?
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    I'm not sure. Matrices is the only thing I don't understand in FP1.
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    I would just multiply A by all the options (a,b,c,d) until I got the identity matrix.
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    (Original post by Sora)
    I'm not sure. Matrices is the only thing I don't understand in FP1.
    Perhaps if we rewrite it:

    A^3= A (A^2) = I

    Hence A^{-1}=...
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    A^-1 = A^2 ?
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    (Original post by Sora)
    A^-1 = A^2 ?
    Yep!
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    Not entirely sure how though. Can you explain please?
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    (Original post by Sora)
    Not entirely sure how though. Can you explain please?
    From A(A^2)=I

    we can premultiply each side of the equation by A^{-1}

    So.

    A^{-1}A(A^2)=A^{-1}I

    Thus, in detail:

    (A^{-1}A)(A^2)=A^{-1}

    (I)(A^2)=A^{-1}

    A^2=A^{-1}

    Obviously, you wouldn't need to put all that detail in, in an answer; I've just included it for your understanding.
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    Is that A(A^-1) = I = A^3?

    then A^-1 = A^2
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    Sort of get it now, thanks.
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    Anyone done any work/learning on n x n matrices?

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