Let A be an nxn matrix. Show that if A^(2) = 0, then I-A is nonsingular and (I-A)^(-1) = I+A
Note that (I - A)(I + A)
= I(I + A) - A(I + A)
= (I - A) - (A + A^2)
= I - A^2
= I - 0, since A^2 = 0
= I.
Hence, I - A is non singular with inverse I + A (since the inverse is unique when it does exist)
