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Mathematics 7 Online
OpenStudy (anonymous):

A^3=0. Prove that (I-A)^3= I+A+A^2. A=Matrix

OpenStudy (jamesj):

Use the binomial theorem, which works without problems here because IA = AI = A

OpenStudy (jamesj):

and check your identity, because I'm not sure it's right.

OpenStudy (jamesj):

(which is a polite way of saying it's false.)

OpenStudy (anonymous):

I dont think we've covered binomial theorem. ah wait. i wrote it wrong

OpenStudy (anonymous):

A^3=0 (I-A)^-1= I+A+A^2

OpenStudy (jamesj):

(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

OpenStudy (jamesj):

Ahh ... you don't need the binomial theorem.

OpenStudy (jamesj):

Multiply both sides by I-A and show that the right-hand side equals the left-hand side.

OpenStudy (anonymous):

wow. i had the step (I-A)(I+a+A^2) with me I just didnt know where it came from. Thanks, you're a life saver

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