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Matrices Question MEI

Matrices.png

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

Thanks,
Sora
Original post by Sora
Matrices.png

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

Thanks,
Sora


Since A3=IA^3=I, what's A1A^{-1} in terms of AA ?
Reply 2
I'm not sure. Matrices is the only thing I don't understand in FP1.
Reply 3
I would just multiply A by all the options (a,b,c,d) until I got the identity matrix.
Original post by Sora
I'm not sure. Matrices is the only thing I don't understand in FP1.


Perhaps if we rewrite it:

A3=A(A2)=IA^3= A (A^2) = I

Hence A1=...A^{-1}=...
Reply 5
A^-1 = A^2 ?
Original post by Sora
A^-1 = A^2 ?


Yep!
Reply 7
Not entirely sure how though. Can you explain please?
Original post by Sora
Not entirely sure how though. Can you explain please?


From A(A2)=IA(A^2)=I

we can premultiply each side of the equation by A1A^{-1}

So.

A1A(A2)=A1IA^{-1}A(A^2)=A^{-1}I

Thus, in detail:

(A1A)(A2)=A1(A^{-1}A)(A^2)=A^{-1}

(I)(A2)=A1(I)(A^2)=A^{-1}

A2=A1A^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.
(edited 11 years ago)
Reply 9
Is that A(A^-1) = I = A^3?

then A^-1 = A^2
(edited 11 years ago)
Reply 10
Sort of get it now, thanks.
Reply 11
Anyone done any work/learning on n x n matrices?

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