Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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