Question

A square matrix A is called nilpotent if Ak = 0 for some k > 0. Prove that if A is
nilpotent, then I + A is invertible.

Answer 1

hey i think i seen this question b4
let me see something

Answer 2

my book's definition is different

Answer 3

they say a square matrix A is said to be nilpotent if A^r=0 for some integer r>=1

Answer 4

ryan its been awhile since i taken this course
do you think the definitions are the same?

Answer 5

well they seem to be different to me

Answer 6

If A is nilpotent, then we have Ak=0 for some k>0.
If Ak=0, then doesn't mean A=0.
if A=0, then I+A=I.
I is invertible since it is the identity matrix.
this sounds good to me lol