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# FP1: Any matrices experts? Matrices Problem Watch

1. Question 6)iv)
http://filestore.aqa.org.uk/subjects...1-QP-JUN12.PDF

Mark Scheme:
http://filestore.aqa.org.uk/subjects...W-MS-JUN12.PDF

I don't understand it, where I = the identity matrix, why does this work...

(-4I)^503 = -(2^2)503I

You can't just move I outside? Sorry for my ignorance.

I think it is because I doesn't affect anything and can be moved anywhere, since anything multiplied by I is the same thing? I don't know.

I just need someone to clarify me and help me understand what I find difficult (and what you may find easy).

Many thanks.
2. (Original post by Konnichiwa)
anything multiplied by I is the same thing?
That's it.
3. aA x aB = a^2 (A x B)

This is easily seen because you will have a factor of a^2 in each term of each sum that makes up every item in the product.

Through a similar reasoning:

aA x aB x aC = a^3 (A x B x C)

aA x aB x aC x aD = a^4 (A x B x C x D)

etc.

(aA)^n = a^n (A^n)

And so, by an application of such:

(aI)^n = (a^n)I^n = (a^n)I
4. Also, it kind of makes sense because of how matrix multiplication works and where the 0s are in the identity matrix.

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