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FP1 Further Maths - Matrix Algebra

Hi there,
If I have two matrices A and B, and I am told to find (A+B)^2, is this the same as A^2 + B^2 + 2(AB) or can it only be done by first adding A and B and then squaring the resultant matrix?
Many thanks!
(edited 6 years ago)
Original post by Martha8
Hi there,
If I have two matrices A and B, and I am told to find (A+B)^2, is this the same as A^2 + B^2 + 2(AB) or can it only be done by first adding A and B and then squaring the resultant matrix?
Many thanks!


Original post by Matt#
Yes it's exactly the same. You will probably find that the latter approach is a lot quicker though.


Yes, you can add A and B and then square the result, and that's probably the easiest way to do it.

BUT this is not the same as A2+B2+2(AB)A^2+B^2 +2(AB), which is incorrect. Matrix multiplication is not in general commutative, AB does not necessarily equal BA.

(A+B)2=(A+B)(A+B)=A2+B2+AB+BA(A+B)^2 = (A+B)(A+B)= A^2 + B^2 + AB + BA
(edited 6 years ago)
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Martha8
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Original post by ghostwalker
Yes, you can add A and B and then square the result, and that's probably the easiest way to do it.

BUT this is not the same as A2+B2+2(AB)A^2+B^2 +2(AB), which is incorrect. Matrix multiplication is not in general commutative, AB does not necessarily equal BA.

(A+B)2=(A+B)(A+B)=A2+B2+AB+BA(A+B)^2 = (A+B)(A+B)= A^2 + B^2 + AB + BA


Of course!
I knew it wasn't right but I couldn't figure out why!
Thank you, can't believe I didn't spot it aha

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